Question 1

You are in a dark room with a deck of 52 cards. You know exactly 10 cards are face up. You can't see or feel which way cards face. Split the deck into two piles so each pile has the same number of face-up cards.

Accepted Answer

Take any 10 cards off the top and flip them over. This pile now has the same number of face-up cards as the remaining 42-card pile. If the top 10 cards had k face-up cards, then the bottom pile has 10-k face-up cards. After flipping all 10, the top pile has 10-k face-up cards too.

Question 2

You have 12 balls, one is heavier or lighter. You have a balance scale and 3 weighings. Find the odd ball and whether it's heavier or lighter.

Accepted Answer

Divide into 3 groups of 4. Weigh group A vs group B. Case 1: they balance — the odd ball is in group C. Take 3 from C, weigh against 3 known-good balls. If they balance, the remaining ball is odd — weigh it against a known ball to determine heavier/lighter. If they don't balance, you know whether the odd ball is heavier or lighter; weigh 2 of the 3 suspects against each other to isolate it. Case 2: A and B don't balance — you now know which side is heavier. Relabel and use the third weighing to isolate the odd ball among the suspects.

Question 3

You have 25 horses and can race 5 at a time. What is the minimum number of races needed to find the 3 fastest horses (no stopwatch)?

Accepted Answer

7 races. First, run 5 races of 5 horses each (5 races). Rank the winners and race them against each other (race 6). Now the overall fastest horse is the winner of race 6. The 2nd and 3rd fastest must be among: the 2nd and 3rd place from the winner's original group, the 2nd place from the group whose winner came 2nd in race 6, and the winner who came 3rd in race 6. That's 5 candidates — race them (race 7). The top 2 from race 7 plus the overall winner are your 3 fastest.

Question 4

You are standing outside a closed room with three light bulbs and three switches. You can flip switches as much as you want but can only enter the room once. How do you determine which switch controls which bulb?

Accepted Answer

Turn on switch 1 and wait 5 minutes. Turn it off, turn on switch 2, and enter. The lit bulb is switch 2. The warm but off bulb is switch 1. The cold, off bulb is switch 3.

Question 5

You have a 3-litre jug and a 5-litre jug with unlimited water. How do you measure exactly 4 litres?

Accepted Answer

Fill the 5L jug, pour into the 3L jug (leaving 2L). Empty the 3L jug, pour the 2L into it. Fill the 5L jug again and pour into the 3L jug until full (1L poured). Exactly 4L remain in the 5L jug.

Question 6

Why are manhole covers round rather than square?

Accepted Answer

A round cover cannot fall through its own opening. A circle has constant diameter regardless of orientation, whereas a square cover could be tilted diagonally and fall through since the diagonal is longer than the side.

Question 7

A single lily pad doubles in size every day. It takes 48 days to cover the entire lake. On which day was the lake half-covered?

Accepted Answer

Day 47. Since the lily pad doubles every day, if it covers the full lake on day 48, it must have been half-covered on day 47.

Question 8

100 prisoners in a line each wear a red or blue hat. Starting from the back, each must guess their hat color. They can see all hats in front but not their own. What strategy guarantees 99 are released?

Accepted Answer

The last prisoner counts blue hats in front and says 'Blue' if even, 'Red' if odd (parity check). Each subsequent prisoner tracks the running parity from previous guesses and what they see ahead to deduce their own hat color. All 99 after the first are guaranteed correct.

Question 9

On a standard analog clock, what is the exact angle between the hour and minute hands at 3:15?

Accepted Answer

7.5 degrees. At 3:15, the minute hand is at the 3 (90 degrees). The hour hand moves 0.5 degrees per minute, so in 15 minutes past 3 it has moved 7.5 degrees beyond the 3. The gap is 7.5 degrees.

Question 10

A blind man has 10 black socks and 10 navy blue socks in a drawer. How many must he pull out to guarantee a matching pair?

Accepted Answer

3 socks. By the Pigeonhole Principle, with only 2 colors, the 3rd sock must match one of the first two.

Question 11

You have two ropes, each burns for exactly 1 hour but not uniformly. How do you measure exactly 45 minutes?

Accepted Answer

Light rope 1 from both ends and rope 2 from one end simultaneously. Rope 1 burns out in 30 minutes. At that moment, light the other end of rope 2. Rope 2 had 30 minutes of burn left, but now burning from both ends it takes 15 more minutes. Total: 30 + 15 = 45 minutes.

Question 12

You have 10 people in a room. How many total handshakes if they all shake hands?

Accepted Answer

45. (10 choose 2) = 10! / (2! × 8!) = 45 — this is the total number of ways two people can shake hands.

Question 13

A group of people wants to determine their average salary on the condition that no individual would be able to find out anyone else's salary. Can they accomplish this, and, if so, how?

Accepted Answer

Yes. The first person thinks of a random number X and adds it to their salary. The rest of the group simply adds their salary to the running total. Then, the first person subtracts X and divides by the group size to get the average.

Question 14

You have a 3 gallon jug and 5 gallon jug, how do you measure out exactly 4 gallons?

Accepted Answer

Fill the 3-gallon jug and pour into the 5-gallon. Fill the 3-gallon again and pour until the 5-gallon is full (1 gallon remains). Empty the 5-gallon, pour in the 1 gallon, then fill the 3-gallon and add it. 1 + 3 = 4 gallons.

Question 15

You're in a room with three light switches, each controls one of three bulbs in the next room. All lights are off. You can only inspect the other room once. How do you determine which switch controls which bulb?

Accepted Answer

Turn switch 2 on for ten minutes, then turn it off and quickly turn on switch 3. Go into the room. The lit bulb is switch 3. The off but warm bulb is switch 2. The remaining cold bulb is switch 1.

Quantitative Finance

Quantitative Finance

Quantitative Finance

Quantitative Finance