162 Logic Puzzles & Brain Teasers With Answers - page 2 of 2
Shortest distance from room corner to opposite corner?
Imagine the room as a flat 2D net. The shortest path is a straight line across two adjacent 'unfolded' faces of the room.
Measure 4L using 3L and 5L jugs.
Fill 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.
Angle between clock hands at 3:15?
At 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�.
3-way. Accuracy 33/50/100. You (33) go first. Action?
If 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.
20% men/40% women attend. 35% employees men. Total %?
Assume 100 people: 35 men, 65 women. Attending: (20% of 35 = 7) + (40% of 65 = 26). 7 + 26 = 33 people total out of 100.
How is world population measured?
It is a combination of national censuses (counting) and statistical sampling/modeling for areas with less reliable data.
Alex (RR/BB wins). Sam (BR/RB wins). Better position?
Variance 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.
7-part bar. Pay 1 part/day for 7 days. Snap twice?
Binary 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.
Weigh an elephant without a massive scale?
Archimedes' 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.
3R, 2B hats. 1st/2nd can't guess. What is 3rd's color?
If 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.
How do you move Mount Fuji?
This tests lateral thinking. You can 'move' it by moving yourself relative to it, or by waiting for continental drift over millions of years.
Double every 5m. 1 fills in 12h. Time for 2 to fill?
Starting 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.
Guess 1-1000 with higher/lower. Max guesses?
Binary search halves the search space each time. 2^10 = 1024, which covers 1-1000 in exactly 10 steps.
Can the mean of two consecutive primes be a prime?
The average of two numbers is the number exactly between them. All numbers between consecutive primes are composite by definition.
Can you swim faster in syrup or water?
The increased friction in syrup is balanced by the increased resistance the water provides for your stroke to push against. Studies (and Mythbusters) confirm this.
6 chambers, 2 consecutive bullets. Fired empty. Spin or stay?
Two 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.
Times digit "3" is printed between 3,000 and 4,000?
The 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.
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.
You measure my life in hours and I serve you by expiring. I'm quick when I'm thin and slow when I'm fat.
A thin candle burns through its length quickly, while a thicker one lasts longer.
I am tall when I'm young and short when I'm old. I can brighten your day unless it's windy.
A candle melts down as it burns; wind can blow its flame out.
I have lakes with no water, mountains with no stone and cities with no buildings.
A map represents these physical features symbolically on paper.
If you drop me I'm sure to crack, but give me a smile and I'll always smile back.
A dropped mirror shatters easily, and a mirror always reflects back whatever expression you show it, including a smile.
I am always hungry and will die if not fed, but whatever I touch will soon turn red.
Fire needs fuel to survive and leaves glowing red embers behind.
I turn once, what is out will not get in. I turn again, what is in will not get out.
Turning a key locks or unlocks a door, controlling entry and exit.
I have lakes with no water, mountains with no stone and cities with no buildings. What am I?
It is a symbolic representation of the earth's surface.
What is cut on a table, but is never eaten?
Commonly used in games of chance and skill like poker.