151 Math Riddles With Answers - page 2 of 2
1) 1 penalty for �1k. 2) 2 of 3 for �1k. Choice?
If 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.
Place coins on round table. Last one wins. Go 1st or 2nd?
By 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.
54 cards (2 Jokers). Probability both are Jokers?
First Joker: 2/54. Second Joker: 1/53. Multiply them: 2 / (54 * 53) = 2 / 2862 = 1 / 1431.
Name 5 uses for a stapler without staples.
Focus on the physical properties of the heavy, hinged metal object rather than its intended function.
14ft pole. Up 5ft day, down 3ft night. Days to top?
The 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.
Owe 49+49=98. Plus your $1 = 99. Where is the dollar?
The error is adding the $1 you kept to the $98 debt. You should subtract it: $98 debt - $1 cash = $97 cost of shirt.
1/1000 trick coin. Flip 10 heads. Prob it's the trick coin?
Bayes' 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.
How can the Earth's mass be measured?
By 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.
Pick 1 of 1000 seats. 990 empty removed. Odds now?
Removing 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).
Price reduced 23%. Increase needed to restore original?
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%.
100B and 100W pearls. Maximize chance of picking Black.
Putting 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%.
How many smartphones are there in London?
With a population around 9 million, and high smartphone penetration among adults and teens, 8 million is a logical estimate.
Two 1-hr ropes, burn inconsistently. Measure 45 mins?
Lighting 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.
Black win $1, Red lose $1. Quit anytime. Strategy?
The expected value changes with every card drawn. If you have drawn more red than black, your chances of winning improve, and vice versa.
Does running keep you drier than walking in rain?
Running reduces the exposure time to falling rain. Even though you 'run into' more drops, the time saved outweighs the front-facing accumulation.
Ascend 9-7 Day 1, descend 9-7 Day 2. Spot reached at same time?
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.
25 horses, 5-horse races. Min races to find top 3?
Race 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.
Flip 4 coins. At least 2 are tails. Probability exactly 3 are tails?
Total outcomes are 16. Out of 16, 11 have >= 2 tails. Out of those 11, exactly 4 outcomes have 3 tails {TTTH, TTHT, THTT, HTTT}.
10R, 20B, 30G socks in 3 sizes. Min pull for matching pair?
There 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.
How many corners (vertices) does a tesseract have?
A 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.
Joey/Charlie share 50ml. Joey sips 1/2, Charlie 1/2 of rest, repeat...
This 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.
Why are manhole covers round?
A square cover can be turned diagonally and dropped through the hole. A circle has a constant diameter and cannot fall in.
Measure 9 mins using 4-min and 7-min hourglasses.
Run 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.
Choice: 1) Roll 1 die for $1M x result. 2) Roll 1M times for $1 x total.
The 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.
Brick thrown from boat into small pond. Does water level change?
When 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.
How many times in 24 hours do clock hands form a 90� angle?
There 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.
20-ton lorry on 20-ton bridge. Bird lands halfway. Does it collapse?
A truck traveling across a bridge burns fuel, losing more weight in liquid fuel than a small bird weighs when landing.
Family has 2 kids, one is a boy. Probability the other is a girl?
The 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}.
5 cats catch 5 mice in 5 mins. Cats needed for 100 mice in 100 mins?
If 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.
100 people flip switches of multiples of their entry. How many stay on?
A 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.
How many gas stations are there in the United States?
This 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.
2 A and 2 B pills identical. Hand has 1A, 2B. How to get correct dose?
By 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.
10x10x10 cube painted then cut into 1x1x1s. How many have no paint?
Removing the outer layer of cubes leaves an inner cube of dimensions (10-2)x(10-2)x(10-2), which is 8x8x8 = 512.
3-pointer (40% win) or 2-pointer (70% tie, then 50% OT win)?
Winning with a 3-pointer is 40%. For the 2-pointer, the win probability is 70% (to tie) * 50% (to win OT) = 35%. 40% > 35%.
9 marbles, one is heavier. Min weighings on a balance to find it?
Divide 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.
What is the sum of all the integers from 1 to 100?
Use the formula for the sum of an arithmetic series: n(n+1)/2. For n=100, it is 100*101/2 = 5,050.
I'm red all over, with dust in the air. Some people think I might have had water to share. What am I?
The fourth planet from the sun, known for its reddish hue.
I'm the planet with the most bling, I've got rings you can't help noticing! What am I?
The gas giant famous for its extensive ring system.
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?
'My father's son' refers to the speaker himself.
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?
Use simple algebra to balance the sibling relationships.
If there are three apples and you take away two, how many apples do you have?
The question asks how many you possess after taking them.
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?
He has one daughter of each hair color.
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?
The phrase means all were destroyed except for those three.
The day before yesterday I was 21, and next year I will be 24. When is my birthday?
The birthday falls on the very last day of the year.
Two fathers and two sons are in a car, yet there are only three people in the car. How?
The three people represent three generations: child, parent, grandparent.
Three doctors said that Bill was their brother. Bill says he has no brothers. How many brothers does Bill actually have?
The doctors are female, making them Bill's sisters.
Which is heavier: a ton of bricks or a ton of feathers?
A ton is a unit of weight; one ton always equals one ton.
Mary has four daughters, and each of her daughters has a brother. How many children does Mary have?
The brother is shared by all the sisters.
What three numbers, none of which is zero, give the same result whether they're added or multiplied?
The sum and the product of these three specific integers are both 6.
If two's company, and three's a crowd, what are four and five?
It's a basic math question disguised as a riddle.
I am an odd number. Take away a letter and I become even. What number am I?
Spell the word 'Seven' and remove the 's'.