Quant brain teasers interviewers actually ask

12 identical-looking balls include exactly one of a different weight — you don’t know if it’s heavier or lighter. Using only a balance scale, what is the minimum number of weighings that guarantees finding the odd ball AND whether it is heavy or light?

You have 1000 bottles of wine, exactly one of which is poisoned. A test strip reacts (after one hour) if it touches any poison. With only one hour before a feast, what is the minimum number of test strips needed to guarantee finding the poisoned bottle?

Three jars are labeled “Apples”, “Oranges”, and “Apples + Oranges”. Every label is wrong. Drawing one fruit at a time without looking, what is the minimum number of draws to correctly relabel all three jars?

Three off switches outside a windowless room each might control the single bulb inside. You may flip switches freely but can enter the room only once. How do you determine which switch controls the bulb?

On an island live 100 blue-eyed people and some brown-eyed people. Nobody knows their own eye colour, everyone sees everyone else’s, and anyone who deduces their own colour must leave that midnight. All islanders are perfect logicians and this is common knowledge. One day a visitor announces to everyone: “At least one of you has blue eyes.” On which night do the blue-eyed islanders leave?

You have 2 identical eggs and a 100-floor building. An egg breaks if dropped from floor F or above. Minimise the number of drops in the worst case needed to find F with certainty. How many drops?

25 horses, a track that races 5 at a time, and no stopwatch. What is the minimum number of races needed to find the 3 fastest horses?

Four people must cross a bridge at night with one flashlight. They take 1, 2, 5 and 10 minutes to cross. At most two cross at once, and a pair moves at the slower person’s pace; the flashlight must be walked back each time. What is the minimum total time (minutes)?

A camel must transport 3,000 bananas across a 1,000 km desert to market. It can carry at most 1,000 bananas at a time and eats 1 banana per km travelled (in either direction). Bananas may be cached anywhere along the route. What is the maximum whole number of bananas that reach the market?

Five rational pirates split 100 gold coins. The most senior proposes a split; if at least half (including the proposer) approve, it passes — otherwise he is thrown overboard and the next-senior proposes. Pirates prioritise survival, then gold, then bloodthirst. How many coins does the most senior pirate keep?

100 lockers start closed. Person i (for i = 1…100) toggles every locker that is a multiple of i. After all 100 people pass, how many lockers are open?

Two diagonally opposite corner squares are removed from a standard 8×8 chessboard, leaving 62 squares. Can the remaining board be exactly tiled by 31 dominoes, each covering two adjacent squares? Answer yes or no.

Three ants sit on the three corners of a triangle. Each independently picks one of the two edges and starts walking. What is the probability that none collide?

At a party of 10 people, everyone shakes hands with everyone else exactly once. How many handshakes happen in total?

You have a 3-gallon jug and a 5-gallon jug and a tap. How do you measure exactly 4 gallons?

What is the sum of the integers from 1 to 100?

How many trailing zeros does 100! (100 factorial) have?

What is the last (units) digit of 2^100?

What is the angle (in degrees) between the hour and minute hands of an analog clock at exactly 3:15?

You have two ropes; each takes exactly 60 minutes to burn end-to-end, but neither burns at a uniform rate. With only a lighter, how do you measure exactly 45 minutes?

Three doors: one hides a car, two hide goats. You pick a door; the host (who knows) opens a different door revealing a goat, then offers you the switch. What is your probability of winning the car if you switch?

A family has two children. Given that at least one is a boy, what is the probability that both are boys?

A family has two children. You learn that at least one of them is a boy born on a Tuesday (assume boys and girls, and all birth days, are equally likely and independent). What is the probability that both children are boys?

100 prisoners’ numbers are placed randomly in 100 boxes, one per box. Each prisoner may open at most 50 boxes, looking for their own number; all must succeed or all die, and they cannot communicate once the search begins. With the optimal strategy (each prisoner starts at their own box and follows the number found to the next box), what is the probability that every prisoner finds their number? Answer to two decimals.

100 passengers board a full 100-seat plane. The first passenger lost their ticket and sits in a uniformly random seat. Each later passenger takes their own seat if free, else a random free seat. What is the probability the 100th passenger sits in their own seat?

You interview 100 candidates in random order, must accept or reject each on the spot, and want the single best. The optimal rule observes and rejects an initial fraction, then takes the first candidate better than everyone seen so far. Roughly what percentage should you observe first?