Back to 151 Math Riddles With Answers

151 Math Riddles With Answers

151 riddles · answers on the last page · riddleup.com/riddles/math-riddles

  1. There are 500 coffins and 500 men who need them. The undertaker asks the first man to go to every coffin and open them. Then he tells the second man to go to every one and close it. The third one goes to every third coffin and so on. How many are open?
  2. How do you go from 98 to 720 using just one letter?
  3. Four years ago, Alex was twice as old as Jake. Four years from now, Jake will be 3/4 of Alex's age. How old is Alex?
  4. If it is two hours later, then it will take half as much time till it's midnight as it would be if it were an hour later. What time is it?
  5. Sally is 54 years old and her mother is 80, how many years ago was Sally's mother three times her age?
  6. If two hours ago, it was as long after one o'clock in the afternoon as it was before one o'clock in the morning, what time would it be now?
  7. In a bicycle race, the man who came two places in front of the last man finished one ahead of the man who came fifth. How many contestants were there?
  8. My daughter has many sisters. She has as many sisters as she has brothers. Each of her brothers has twice as many sisters as brothers. How many sons and daughters do I have?
  9. One brick is one kilogram and half a brick heavy. What is the weight of one brick?
  10. Place three matches on a table. Tell a friend to add two more matches to make eight.
  11. There are 25 red balls, 47 green balls and 3 blue balls in a basket. There is a blind man. What is the minimum number of balls that the blind man has to pick to make sure that there are at least 2 balls of different colors?
  12. Use the numbers 2, 3, 4 and 5 and the symbols + and = to make a true equation.
  13. Mr. Smith has 4 daughters. Each of his daughters has a brother. How many children does Mr. Smith have?
  14. How can you add eight 8's to get the number 1000?
  15. Three times what number is no larger than two times that same number?
  16. The combined age of Jack and John is 49. Jack is twice as old, as John was when Jack was as old as John is now. How old are the brothers?
  17. How many days are there in 4 years?
  18. What is the value of 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 1000?
  19. If you toss a coin 10 times and it lands heads up every time, what are the chances it will land heads up if you toss it again?
  20. In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half the lake?
  21. Dean Sam and Castiel are three brothers. Interestingly their current age is prime. What's more interesting that difference between their ages is also prime. How old are they?
  22. There are two fathers and two sons. They walk into a candy store and each buys a candy bar for 50 cents. The total for all of the candy bars was $1.50. How is that possible?
  23. What number do you get when you multiply all of the numbers on a telephone's number pad?
  24. How can you give someone $83 using exactly 7 bills, without using any one dollar bills?
  25. If Mr. Flynn is 90 centimeters plus half his height, how tall is he?
  26. Divide 20 by half and add 30, what do you get?
  27. There are 12 kids in a classroom. 6 kids are wearing socks and 4 are wearing shoes. 3 kids are wearing both. How many are bare feet?
  28. When I take five and add six, I get eleven, but when I take six and add seven, I get one. What am I?
  29. A bat and a ball cost $1.10. The bat costs one dollar more than the ball. How much does the ball cost?
  30. What 3 positive numbers give the same result when multiplied and added together?
  31. When is 1500 plus 20 and 1600 minus 40 the same thing?
  32. Payoff 2n (St. Petersburg). Charge to play?
  33. Rule: Circle=Yellow. Cards: C, S, Y, R. Check?
  34. Probability to be the last to try pitcher?
  35. Surprise test impossible logic?
  36. Sphere or Torus using rocks?
  37. 9 correct predictions in a row. Psychic?
  38. Describe a chicken in computer programming.
  39. Hourglass weigh more falling or at rest?
  40. Pays payout in Yen. Charge to play?
  41. 5 black spins. Is red "due"?
  42. 10 pennies in 3 cups, each has odd number.
  43. Spoon tea into coffee, mix, spoon back. More what?
  44. Max slices from 4 straight cuts?
  45. Ways to arrange 8 books on a shelf?
  46. 1 poisoned bottle in 1000. Prisoners needed?
  47. P1 (4 of kind), P2 (3 of kind). Worst possible hand?
  48. Break stick at 2 random points. Triangle prob?
  49. Monkey climbs rope with matching weight. Weight?
  50. Reverses left/right but not up/down?
  51. Camel 3000 bananas, 1k km. Max reach?
  52. Get fair toss from biased coin.
  53. Spheres with 6cm holes. Which has more volume?
  54. 200 fish, 99% Gold. Remove how many for 98%?
  55. Brothers Chris (FL) and Connor (OR) same time. How?
  56. Irrational number ^ irrational power = rational?
  57. 1st sits random. Last gets assigned seat prob?
  58. Does washer hole expand or shrink when heated?
  59. How many barbershops are in the USA?
  60. 100 cheating husbands. Execution day?
  61. Truth 3/4 times. Says 6 on a die. Prob it's a 6?
  62. 5 bandits split 100 coins. Senior proposal?
  63. Families stop childbearing after 1st boy. Sex ratio?
  64. How many squares on an 8x8 chessboard?
  65. How many ping pong balls fill a 747?
  66. C beats T by 10m in 100m. C starts 10m back. Winner?
  67. Does level change when ice in water melts?
  68. 4 people: 1, 2, 5, 10 mins. Bridge (max 2). Min time?
  69. 31 games in elimination tournament. Players?
  70. 3 doors: Heaven, 1-day Hell, 2-day Hell. Avg days?
  71. 110m rope. 1ft slack added/pulled up. Truck fits?
  72. Which is greater: e? or ?e?
  73. Surgeon with 2 gloves must operate on 3 patients. How?
  74. Duck in pond. Cat runs 4x faster on edge. Escape?
  75. 1/2 of 2/3 of 3/4... of 9/10 of 1,000?
  76. Pick 1 of 3. Empty removed. Do you switch?
  77. Explain a database to an 8-year-old.
  78. Standard deviation of {1, 2, 3, 4, 5}?
  79. 1/4 into tunnel. Meet train at start or end. Speed ratio?
  80. Sum of digits from 1 to 1,000,000?
  81. Helium balloon in car accelerating forward. Direction?
  82. HH = Jamie takes 2. Any other = Ashley takes 1. Winner?
  83. 100 ants on 1m stick at 1cm/s. Max time to clear?
  84. Shortest distance from room corner to opposite corner?
  85. Measure 4L using 3L and 5L jugs.
  86. Angle between clock hands at 3:15?
  87. 3-way. Accuracy 33/50/100. You (33) go first. Action?
  88. 20% men/40% women attend. 35% employees men. Total %?
  89. How is world population measured?
  90. Alex (RR/BB wins). Sam (BR/RB wins). Better position?
  91. 7-part bar. Pay 1 part/day for 7 days. Snap twice?
  92. Weigh an elephant without a massive scale?
  93. 3R, 2B hats. 1st/2nd can't guess. What is 3rd's color?
  94. How do you move Mount Fuji?
  95. Double every 5m. 1 fills in 12h. Time for 2 to fill?
  96. Guess 1-1000 with higher/lower. Max guesses?
  97. Can the mean of two consecutive primes be a prime?
  98. Can you swim faster in syrup or water?
  99. 6 chambers, 2 consecutive bullets. Fired empty. Spin or stay?
  100. Times digit "3" is printed between 3,000 and 4,000?
  101. 1) 1 penalty for �1k. 2) 2 of 3 for �1k. Choice?
  102. Place coins on round table. Last one wins. Go 1st or 2nd?
  103. 54 cards (2 Jokers). Probability both are Jokers?
  104. Name 5 uses for a stapler without staples.
  105. 14ft pole. Up 5ft day, down 3ft night. Days to top?
  106. Owe 49+49=98. Plus your $1 = 99. Where is the dollar?
  107. 1/1000 trick coin. Flip 10 heads. Prob it's the trick coin?
  108. How can the Earth's mass be measured?
  109. Pick 1 of 1000 seats. 990 empty removed. Odds now?
  110. Price reduced 23%. Increase needed to restore original?
  111. 100B and 100W pearls. Maximize chance of picking Black.
  112. How many smartphones are there in London?
  113. Two 1-hr ropes, burn inconsistently. Measure 45 mins?
  114. Black win $1, Red lose $1. Quit anytime. Strategy?
  115. Does running keep you drier than walking in rain?
  116. Ascend 9-7 Day 1, descend 9-7 Day 2. Spot reached at same time?
  117. 25 horses, 5-horse races. Min races to find top 3?
  118. Flip 4 coins. At least 2 are tails. Probability exactly 3 are tails?
  119. 10R, 20B, 30G socks in 3 sizes. Min pull for matching pair?
  120. How many corners (vertices) does a tesseract have?
  121. Joey/Charlie share 50ml. Joey sips 1/2, Charlie 1/2 of rest, repeat...
  122. Why are manhole covers round?
  123. Measure 9 mins using 4-min and 7-min hourglasses.
  124. Choice: 1) Roll 1 die for $1M x result. 2) Roll 1M times for $1 x total.
  125. Brick thrown from boat into small pond. Does water level change?
  126. How many times in 24 hours do clock hands form a 90� angle?
  127. 20-ton lorry on 20-ton bridge. Bird lands halfway. Does it collapse?
  128. Family has 2 kids, one is a boy. Probability the other is a girl?
  129. 5 cats catch 5 mice in 5 mins. Cats needed for 100 mice in 100 mins?
  130. 100 people flip switches of multiples of their entry. How many stay on?
  131. How many gas stations are there in the United States?
  132. 2 A and 2 B pills identical. Hand has 1A, 2B. How to get correct dose?
  133. 10x10x10 cube painted then cut into 1x1x1s. How many have no paint?
  134. 3-pointer (40% win) or 2-pointer (70% tie, then 50% OT win)?
  135. 9 marbles, one is heavier. Min weighings on a balance to find it?
  136. What is the sum of all the integers from 1 to 100?
  137. I'm red all over, with dust in the air. Some people think I might have had water to share. What am I?
  138. I'm the planet with the most bling, I've got rings you can't help noticing! What am I?
  139. A man looks at a painting in a museum and says, "Brothers and sisters I have none, but that man's father is my father's son." Who is in the painting?
  140. A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?
  141. If there are three apples and you take away two, how many apples do you have?
  142. A man describes his daughters, saying, "They are all blonde, but two; all brunette but two; and all redheaded but two." How many daughters does he have?
  143. A little girl goes to the store and buys one dozen eggs. As she is going home, all but three break. How many eggs are left unbroken?
  144. The day before yesterday I was 21, and next year I will be 24. When is my birthday?
  145. Two fathers and two sons are in a car, yet there are only three people in the car. How?
  146. Three doctors said that Bill was their brother. Bill says he has no brothers. How many brothers does Bill actually have?
  147. Which is heavier: a ton of bricks or a ton of feathers?
  148. Mary has four daughters, and each of her daughters has a brother. How many children does Mary have?
  149. What three numbers, none of which is zero, give the same result whether they're added or multiplied?
  150. If two's company, and three's a crowd, what are four and five?
  151. I am an odd number. Take away a letter and I become even. What number am I?

Answers

  1. 22Only coffins with an odd number of divisors stay open in the end - the perfect squares - and there are exactly 22 perfect squares (1 squared through 22 squared) at or below 500.
  2. Add an "x" between "ninety" and "eight": Ninety x Eight = 720Spelling out "98" as "ninety eight" and inserting the letter x between the words creates "ninety x eight," which multiplies to 720.
  3. 12Solving the two age equations together shows Jake is currently 8 and Alex is currently 12.
  4. Nine (9:00 pm).Working the algebra backward from midnight shows the current time must be 9 o'clock for the stated ratio to hold true.
  5. Forty-one years ago.Solving 80-x = 3(54-x) gives x = 41, so 41 years ago Sally's mother was exactly three times her age.
  6. Nine (9:00 pm).Working backward from "two hours ago," the elapsed time since 1 p.m. must equal the time remaining until 1 a.m., which only balances when the current time is 9 p.m.
  7. There were 6 contestants. The man came in 4th place.If he's two places ahead of last (6th) he's in 4th, and finishing one ahead of 5th place also places him in 4th -- both conditions align only when there are 6 total contestants.
  8. Four daughters and three sons. Each daughter has 3 sisters and 3 brothers, and each brother has 2 brothers and 4 sisters.With 4 daughters and 3 sons, each daughter has 3 sisters and 3 brothers (equal), and each son has 2 brothers and 4 sisters (twice as many sisters as brothers) -- satisfying both conditions.
  9. One brick weighs 2 kilograms.If one brick equals 1 kg plus half a brick, then half a brick must weigh 1 kg, making a whole brick weigh 2 kg.
  10. Add two matches to make a roman numeral eight (VIII).Three matches placed together can form the Roman numeral III; adding two more matches in a 'V' shape in front makes VIII, the Roman numeral for eight.
  11. 48 balls. There is a small chance he may pick up 47 green balls in a row.In the worst possible case, the blind man could draw all 47 green balls in a row before finally getting a red or blue one, so 48 draws guarantee at least two different colors.
  12. 2 + 5 = 3 + 4Both sides of the equation 2 + 5 = 3 + 4 equal 7, satisfying the challenge using each of the four given numbers exactly once.
  13. FiveSince "each of his daughters has a brother" refers to the same single brother shared by all four daughters, Mr. Smith has 4 daughters plus 1 son, for 5 children total.
  14. 888 + 88 + 8 + 8 + 8 = 1000Try combining the 8's into different-length numbers (888, 88, 8) rather than adding eight separate 8's.
  15. 0Only when the number is zero does tripling it (still zero) stay no larger than doubling it (also zero); for any positive number, tripling it would exceed doubling it.
  16. Jack is 28 and John is 21.Jack's age (28) is twice what John's age was seven years ago (14), which is exactly the gap between their ages now (28 - 21 = 7), and 28 + 21 = 49 as required.
  17. 1461. (365 x 4) + 1, because one of the years is a leap year.Four years of 365 days would total 1,460 days, but one of the four is a leap year with an extra day, bringing the true total to 1,461.
  18. 100.Multiplying the fraction chain 1/2 x 2/3 x 3/4 ... x 9/10 causes every numerator and denominator to cancel except the very first and last, leaving 1/10 of 1000, which is 100.
  19. There is a 50/50 chance of each toss being either heads or tails. The previous toss does not impact the next toss.A fair coin has no memory -- each flip is an independent event with exactly a 50% chance of heads, regardless of past results.
  20. The patch doubles in size every day, so on the 47th day the patch will be half the size it is on the 48th day.Since the patch's size doubles every single day, it must have covered exactly half the lake just one day before it covered the whole lake - day 47.
  21. Sam is 2, Dean is 5, and Castiel is 7. The age differences (5-2=3, 7-5=2, 7-2=5) are all prime numbers.Ages 2, 5, and 7 are all prime numbers, and the differences between them - 3, 2, and 5 - are also all prime, satisfying every condition in the riddle.
  22. There was a grandfather, a father and a son.With a grandfather, father, and son, the middle person counts as both a father and a son, giving 'two fathers and two sons' among only three people who buy just three candy bars.
  23. Zero. Anything multiplied by 0 will equal 0.Every phone keypad includes the digit 0, and multiplying any set of numbers that includes zero always results in zero.
  24. Give them 1 fifty dollar bill, 1 twenty dollar bill, 1 five dollar bill and 4 two dollar bills.A $50 bill, a $20 bill, a $5 bill, and four $2 bills together total $83 using exactly seven bills and no $1 bills.
  25. 180 centimeters.If 90 cm equals half his height, his full height must be double that, or 180 centimeters.
  26. 70. 20 divided by 1/2 is 40, plus 30 equals 70.Dividing 20 by one-half means multiplying by 2, giving 40; adding 30 brings the total to 70.
  27. 5 kids are bare feet.Adding the sock-wearers and shoe-wearers together and subtracting those double-counted for wearing both (6 + 4 - 3 = 7) leaves 12 - 7 = 5 kids with bare feet.
  28. A clockThis is a clock-face riddle: five o'clock plus six hours lands on eleven, but six o'clock plus seven hours wraps back around to one on a 12-hour clock.
  29. The ball costs 5 cents, not 10 cents. One dollar more than 10 cents is $1.10, but $1.10 + 10 cents would be $1.20. One dollar more than 5 cents is $1.05, and the sum of that is $1.10.If the ball costs 5 cents, the bat costs $1.05 (one dollar more), and together they total $1.10 -- the common wrong intuitive answer of 10 cents doesn't satisfy the 'one dollar more' condition.
  30. 1, 2 and 31 + 2 + 3 = 6 and 1 x 2 x 3 = 6, making them the only three positive numbers whose sum and product are equal.
  31. Military time (both equal 1520)In 24-hour (military) time, 1500 plus 20 minutes is 1520, and 1600 minus 40 minutes is also 1520 -- both calculations land on the same time, 3:20 PM.
  32. Small amountThe mathematical expectation is infinite, but most people wouldn't pay more than �20. This illustrates that humans value money based on 'utility' rather than just the raw expected amount.
  33. Circle and RedYou check the Circle (to see if back is Yellow) and the Red card (to see if front is a Circle, which would break the rule). Yellow and Square can't invalidate the rule.
  34. 1/n (Equal)This is a property of a 'random walk' on a circle. Every person is equally likely to be the last one reached before the circle is completed.
  35. ParadoxIf the test hasn't happened by Thursday, the students know it must be Friday (so it's not a surprise). This logic continues backward to Monday, 'proving' it can never be a surprise.
  36. Perpendicular loopsOn a sphere, any two 'great circles' must intersect. On a torus, you can have a loop that goes around the center and another through the hole that never meet.
  37. NoThe company sends 5,000 emails: 2,500 say Team A wins, 2,500 say Team B. They keep splitting the winners until one small group (like Kelly) has seen a perfect streak.
  38. A functionIn coding, a function is something that takes an input and provides an output. Grain is the parameter, and the Egg is the return value.
  39. More while fallingWhen sand is in the air, its weight isn't recorded by the scale. However, the force of the sand hitting the bottom is greater than its static weight, resulting in a net increase during the flow.
  40. > �3.50The expected value is the average of all outcomes: (1+2+3+4+5+6)/6 = 21/6 = 3.5. To make a profit, the 'house' must charge more than the expected payout.
  41. NoThe roulette wheel has no memory. Each spin is a fresh event with the same probability (ignoring the green zero), regardless of what happened before.
  42. Nesting cupsPut 1 in the first, 1 in the second, and 8 in the third... but wait, the trick is nesting. Put 1 in cup A, 2 in cup B, and nest B inside cup C (which has 7). Now C has 9 (odd).
  43. Exactly sameSince you started and ended with the same volume in each cup, any 'tea' that stayed in the coffee must have been replaced by an exactly equal volume of 'coffee' in the tea.
  44. 11 slicesThe formula is (n^2 + n + 2) / 2. For n=4, that is (16 + 4 + 2) / 2 = 11. This assumes cuts can overlap and pass through previous cuts.
  45. 40320The number of permutations is n factorial (n!). For 8 books, it is 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320.
  46. 10 prisonersGive each prisoner a unique combination of bottles to sip from based on binary (0 and 1). The specific combination of prisoners who get sick creates a binary code for the poisoned bottle number.
  47. 3 of kindIf Player 1 has four of a kind and Player 2 has three of a kind, there must be at least three cards of the same rank on the shared board. Your hand will use those same three cards.
  48. 2026-01-04Using the 'triangle inequality' theorem, no piece can be longer than 0.5m. Visualizing this on a 2D plot of possible break points shows the 'success' area is 1/4 of the total area.
  49. Rises with monkeyThe force the monkey exerts to climb increases the tension in the rope equally on both sides. Thus, both the monkey and the counterweight accelerate upward together.
  50. Inverts Z-axisIf you point your finger to the right, the mirror image points to the right. The reversal is actually in the 'depth' (front to back) dimension relative to the mirror's surface.
  51. 533.3 bananasThe camel must leave 'caches' of bananas. To minimize the 'cost' of travel, he moves the bananas in stages until the total supply matches his max capacity for the remaining distance.
  52. Toss twiceIf you toss twice, the probabilities of HT and TH are both (p * (1-p)). Since these are equal, assigning one to 'Heads' and the other to 'Tails' creates a fair 50/50 result.
  53. Exactly sameThe volume of a spherical ring depends only on the height of the hole (h). The formula V = (pi * h^3) / 6 shows the radius (R) of the original sphere cancels out.
  54. 100 goldfishIn 200 fish, 198 are gold (99%). To make them 98%, the 2 non-goldfish must represent 2% of the total. 2 is 2% of 100. So you must have 100 fish total (remove 100 gold).
  55. Time zone patchesFlorida has a tiny portion in Central Time, and Oregon has a portion in Mountain Time. During the DST 'fall back' hour, the times can align perfectly across the country.
  56. YesConsider x = sqrt(2)^sqrt(2). If x is rational, we are done. If x is irrational, then x^sqrt(2) = (sqrt(2)^sqrt(2))^sqrt(2) = sqrt(2)^2 = 2, which is rational.
  57. 2026-01-02This is a classic probability puzzle. Either the first person takes your seat, or they take their own, or they take someone else's which triggers a chain that eventually hits yours or theirs.
  58. ExpandsThermal expansion is like a photographic enlargement. Every part of the object, including the 'empty' hole, expands proportionally.
  59. 130000Estimate based on one barber per ~2,500 people. With a US population of 330 million, 130,000 is a standard Fermi estimation result.
  60. Day 100If there was 1 cheater, his wife would know immediately. If 2, they wait to see if the other wife acts. By the 100th day, the lack of action by others proves your own husband is one.
  61. 2026-03-08The probability he says 6 AND it is 6 is (1/6 * 3/4). The probability he says 6 but it isn't 6 is (5/6 * 1/4). Use Bayes to find the ratio.
  62. 98:0:1:0:1The senior bandit knows he only needs two other people to agree. He offers 1 coin to those who would get nothing in the next-best scenario to secure their vote.
  63. 01:01:00Every individual birth has a 50/50 chance. No matter the 'stopping rule,' the total expected number of boys and girls in the population will remain equal.
  64. 204 squaresDon't just count the 1x1 squares. You must sum all possible sizes: 1x1 (64), 2x2 (49), 3x3 (36), 4x4 (25), 5x5 (16), 6x6 (9), 7x7 (4), and 8x8 (1).
  65. ~4.2 millionEstimate the volume of a 747 (approx 1000 m^3) and the volume of a ping pong ball, then account for the 'packing fraction' of empty air space between balls.
  66. ChandlerSince Chandler runs 100m in the same time Toni runs 90m, when Chandler is 10m back, they will meet at the 90m mark. Chandler is faster and will pull ahead in the last 10m.
  67. UnchangedAccording to Archimedes, the floating ice displaces a volume of water equal to its weight. When it melts, it becomes water of that exact weight and volume.
  68. 15 minutesFastest pair (1&2) cross (2m), 1 returns (1m), slowest pair (5&10) cross (10m), 2 returns (2m), fastest pair (1&2) cross again (2m). 2+1+10+2+2 = 17m? Wait, logic says 15m is possible.
  69. 32 playersIn any knockout tournament, every player except the winner must lose exactly one game to be eliminated. If there were 31 games, 31 people lost.
  70. 3 daysE = 1/3(0) + 1/3(1+E) + 1/3(2+E). Solving for E: E = 1 + 2/3E -> 1/3E = 1 -> E = 3.
  71. Yes (4.1m high)Adding 1ft of slack to 110m (360ft) creates a triangle with base 180 and hypotenuse 180.5. sqrt(180.5^2 - 180^2) = 13.4 ft, plenty for a truck.
  72. e?Take the e-th root of both. e^(1/e) is the maximum value for the function x^(1/x). Since e is the base of the maximum, e^pi > pi^e.
  73. Layer/ReversePatient 1: Gloves A and B. Patient 2: Only Glove B (top one removed). Patient 3: Turn Glove A inside out and put it over B. A's clean side is now outside.
  74. YesThe duck swims in a circle of radius R/4. The cat has to run halfway around the pond (pi * R). The duck's distance is shorter than the cat's travel time allows for.
  75. 100The series is (1/2)*(2/3)*(3/4)*...*(9/10). The numerators and denominators cancel out diagonally, leaving 1/10. 1/10 * 1,000 = 100.
  76. YesYour initial pick had a 1/3 chance. The remaining 2/3 chance is now concentrated in the one unopened envelope the interviewer didn't discard.
  77. Toy shelfUse a metaphor of an organized filing system or library where everything has a specific label and 'shelf' to make it easy to find later.
  78. 1.414 (2?)The mean is 3. Squares of deviations: (1-3)^2=4, (2-3)^2=1, (3-3)^2=0, (4-3)^2=1, (5-3)^2=4. Average is 10/5 = 2. SD is sqrt(2) ? 1.414.
  79. Train is 2x fasterIf she meets the train at the end after running 3/4 of the way, and she would have met it at the start after running 1/4 back... set up the time/distance equations.
  80. 27000001The sum for 0-999,999 is (sum of digits 0-9) * (number of positions) * (frequency). 45 * 6 * 100,000 = 27,000,000. Add 1 for the '1' in 1,000,000.
  81. ForwardIn an accelerating car, heavier air is pushed to the back. This creates a pressure gradient that 'buoys' the lighter helium balloon toward the front.
  82. AshleyThere are 4 outcomes: HH, HT, TH, TT. HH (Jamie) happens 1/4. HT, TH, TT (Ashley) happen 3/4. Ashley wins 3 times for every 1 time Jamie wins (actually 3 coins to Jamie's 2).
  83. 100 secondsBecause all ants are identical, a 'bounce' is mathematically the same as two ants passing through each other. The max time is just the time for the furthest ant to walk to the end.
  84. ~2.236 unitsImagine the room as a flat 2D net. The shortest path is a straight line across two adjacent 'unfolded' faces of the room.
  85. Fill/pour sequenceFill 3, pour into 5. Fill 3 again, pour into 5 until full. 1L remains in the 3L jug. Empty 5, put that 1L in. Fill 3 and add to the 5L jug to get 4L.
  86. 7.5At 3:15, the minute hand is at 15m (90�). The hour hand has moved 1/4 of the way between 3 and 4. 30� per hour * 0.25 = 7.5�.
  87. Shoot in the airIf you miss on purpose, the 50% shooter will try to kill the 100% shooter (his biggest threat). This leaves you a 1-on-1 duel against a surviving, possibly weaker, opponent.
  88. 0.33Assume 100 people: 35 men, 65 women. Attending: (20% of 35 = 7) + (40% of 65 = 26). 7 + 26 = 33 people total out of 100.
  89. Census/SamplingIt is a combination of national censuses (counting) and statistical sampling/modeling for areas with less reliable data.
  90. SamVariance measures risk. Sam's payouts are always �2 for mixed colors, while Alex fluctuates between �3 and �1. Lower variance is 'safer' for the same return.
  91. Snap into 1, 2, 4Binary counting: Pieces of 1, 2, and 4 units can be combined to form any total from 1 to 7. You swap pieces with the gardener daily like giving change.
  92. Water displacementArchimedes' Principle: Put the elephant on a boat, mark the water line. Remove elephant and add stones until the boat hits the same line. Weigh the stones.
  93. RedIf the 3rd professor saw two blue hats, he would know his is red (only 2 blue exist). Since he doesn't know, the others must have at least one red hat... follow the deduction chain.
  94. Creative answersThis tests lateral thinking. You can 'move' it by moving yourself relative to it, or by waiting for continental drift over millions of years.
  95. 11h 55mStarting with 2 is exactly where the 1-bacterium pond would be after 5 minutes (first doubling). So it saves 5 minutes off the 12-hour total.
  96. 10 guessesBinary search halves the search space each time. 2^10 = 1024, which covers 1-1000 in exactly 10 steps.
  97. NoThe average of two numbers is the number exactly between them. All numbers between consecutive primes are composite by definition.
  98. Roughly sameThe increased friction in syrup is balanced by the increased resistance the water provides for your stroke to push against. Studies (and Mythbusters) confirm this.
  99. Fire againTwo bullets in 6 chambers leaves 4 empty slots. Since you just fired an empty one, there are 5 slots left; only one of the empty slots is followed by a bullet. 1/4 chance vs 1/3 if you spin.
  100. 1,300 timesThe digit 3 appears 1,000 times in the thousands place (3000-3999) and 100 times in each of the other three places (hundreds, tens, units) within that range.
  101. 2 of 3 if prob > 0.5If your skill (P) is > 0.5, the more trials you have, the more likely you are to succeed. If P < 0.5, take the single shot to maximize luck.
  102. FirstBy going first and occupying the exact center, you can mirror any move the opponent makes on the opposite side of the table until they run out of space.
  103. 1/1431First Joker: 2/54. Second Joker: 1/53. Multiply them: 2 / (54 * 53) = 2 / 2862 = 1 / 1431.
  104. Creative answersFocus on the physical properties of the heavy, hinged metal object rather than its intended function.
  105. 6 daysThe net gain is 2ft per 24-hr cycle. After 5 days, it is at 10ft. On the 6th day, it climbs 5ft to reach 15ft (crossing the 14ft mark) before the night slide.
  106. No missing dollarThe error is adding the $1 you kept to the $98 debt. You should subtract it: $98 debt - $1 cash = $97 cost of shirt.
  107. ~1/2Bayes' Theorem: Prior prob of trick coin is 0.001. Prob of 10 heads given trick is 1. Given fair is (1/2)^10 = 1/1024. These are almost equal, so probability is about 0.5.
  108. Gravitation lawBy observing the gravitational pull (g) on the surface and knowing the Earth's radius, we can solve for M in the formula g = G * M / r^2.
  109. 1/1,000Removing empty seats you didn't pick doesn't change the fact that you had a 1-in-1000 chance at the start. The prize is still where it was (or wasn't).
  110. ~30% (29.9%)If a $100 item drops to $77, you need to increase it by $23. $23 divided by $77 is approximately 0.2987, or 29.9%.
  111. 1B in Sack 1; rest in Sack 2Putting 1 black pearl in Sack A gives a 100% chance if A is picked. Sack B then has 99B/100W (~50%). Total chance: 0.5(1) + 0.5(0.497) = 74.85%.
  112. ~8 millionWith a population around 9 million, and high smartphone penetration among adults and teens, 8 million is a logical estimate.
  113. Light ends of R1, 1 end of R2Lighting both ends of a 60m rope makes it burn in 30m. By lighting one end of Rope 2 at the same time, it has 30m left when Rope 1 finishes. Lighting its other end then gives 15m.
  114. Quit at positive EVThe expected value changes with every card drawn. If you have drawn more red than black, your chances of winning improve, and vice versa.
  115. YesRunning reduces the exposure time to falling rain. Even though you 'run into' more drops, the time saved outweighs the front-facing accumulation.
  116. Yes (100%)Intermediate Value Theorem: If you overlay the two trips on the same day, the climber going up and the one going down must meet at some point.
  117. 7 racesRace 5 groups of 5. Race the 5 winners (Race 6). Only the winner of Race 6, 2nd/3rd of that race, and specific others from their groups can be top 3. Race 7 decides.
  118. 2026-04-11Total outcomes are 16. Out of 16, 11 have >= 2 tails. Out of those 11, exactly 4 outcomes have 3 tails {TTTH, TTHT, THTT, HTTT}.
  119. 10 socksThere are 3 colors and 3 sizes = 9 unique combinations. In the worst case, you pull 9 different ones. The 10th must match one of the previous nine.
  120. 16 cornersA point (0D) has 1 vertex. A line (1D) has 2. A square (2D) has 4. A cube (3D) has 8. Doubling each dimension, a tesseract (4D) has 16.
  121. Joey: 33.3ml, Charlie: 16.6mlThis forms a geometric series: Joey = 1/2 + 1/8 + 1/32... Charlie = 1/4 + 1/16 + 1/64... Summing them gives Joey 2/3 and Charlie 1/3 of the total.
  122. Won't fall throughA square cover can be turned diagonally and dropped through the hole. A circle has a constant diameter and cannot fall in.
  123. Flip 4 at 4m, 7 at 7m, 7 at 8mRun both. When 4 ends, 3 mins are left in 7. Flip 4. When 7 ends (7m total), 1 min is left in 4. Flip 7. When 4 ends (8m total), 1 min has run into 7. Flip 7 back to get that 1m.
  124. Game TwoThe law of large numbers ensures Game Two will stay close to the expected value of $3.5M. Game One is high risk; you could end up with only $1M.
  125. Water level dropsWhen in the boat, the brick displaces its weight in water. When in the pond, it only displaces its volume. Since it is denser than water, its volume displacement is less than its weight displacement.
  126. 44 timesThere are 22 such instances in 12 hours (2 per hour, but reduced by overlapping positions at 3 and 9). Thus, 44 times in 24 hours.
  127. NoA truck traveling across a bridge burns fuel, losing more weight in liquid fuel than a small bird weighs when landing.
  128. 2026-02-03The possibilities for two children are {BB, BG, GB, GG}. Knowing one is a boy eliminates GG. The remaining set is {BB, BG, GB}. Two of these have a girl: {BG, GB}.
  129. 5 catsIf 5 cats take 5 minutes for 5 mice, then 1 cat takes 5 minutes for 1 mouse. In 100 minutes, that 1 cat can catch 20 mice. To catch 100, you need 5 cats.
  130. 10 bulbsA bulb ends up 'on' if its switch is flipped an odd number of times. Only numbers with an odd number of divisors (perfect squares) satisfy this.
  131. 160000This is a Fermi problem. Based on a population of 330 million and roughly 1 station per 2,000-2,500 people, 160,000 is a standard estimate.
  132. Add 1A, split all in halfBy adding another A pill, you have 2 A's and 2 B's. Cutting each in half and taking one half of each ensures you get exactly 1 A and 1 B total.
  133. 512 cubesRemoving the outer layer of cubes leaves an inner cube of dimensions (10-2)x(10-2)x(10-2), which is 8x8x8 = 512.
  134. Three-pointerWinning with a 3-pointer is 40%. For the 2-pointer, the win probability is 70% (to tie) * 50% (to win OT) = 35%. 40% > 35%.
  135. Two weighingsDivide marbles into three groups of three. Weigh two groups. If they balance, the heavy marble is in the third group. Then repeat with the remaining three.
  136. 5050Use the formula for the sum of an arithmetic series: n(n+1)/2. For n=100, it is 100*101/2 = 5,050.
  137. MarsThe fourth planet from the sun, known for its reddish hue.
  138. SaturnThe gas giant famous for its extensive ring system.
  139. The man's son'My father's son' refers to the speaker himself.
  140. Four sisters and three brothersUse simple algebra to balance the sibling relationships.
  141. You have two apples.The question asks how many you possess after taking them.
  142. Three: A blonde, a brunette and a redheadHe has one daughter of each hair color.
  143. ThreeThe phrase means all were destroyed except for those three.
  144. December 31; today is January 1.The birthday falls on the very last day of the year.
  145. They are a grandfather, father and son.The three people represent three generations: child, parent, grandparent.
  146. None. He has three sisters.The doctors are female, making them Bill's sisters.
  147. Neither?they both weigh a ton.A ton is a unit of weight; one ton always equals one ton.
  148. Five?each daughter has the same brother.The brother is shared by all the sisters.
  149. One, two and threeThe sum and the product of these three specific integers are both 6.
  150. NineIt's a basic math question disguised as a riddle.
  151. SevenSpell the word 'Seven' and remove the 's'.