Campus Puzzles & Guesstimates

You have 8 identical-looking balls; one is heavier. A balance scale gives you the heavier side. Find the heavy ball in minimum weighings.

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

Three switches outside a room control one bulb inside. You may enter the room only once. Identify the correct switch.

Three doors, one car, two goats. You pick door 1; the host, who knows where the car is, opens a goat door among the remaining two and offers a switch. Should you?

5 pirates (P5 most senior) split 100 coins. Rules: the proposer suggests a split; if at least half (including himself) vote yes it passes, else he is thrown overboard and the next proposes. Pirates are perfectly logical, want to survive, then maximize coins, then prefer throwing others overboard. What does P5 propose?

Two ropes each burn for exactly 60 minutes but unevenly (half the length may burn in 5 minutes). Measure exactly 45 minutes using only the ropes and a lighter.

You have an unmarked 3-litre and 5-litre jug and unlimited water. Measure exactly 4 litres.

Four people cross a night bridge with one torch, at most two at a time. Speeds: 1, 2, 5, 10 min. Pair moves at the slower's pace. Total time ≤ 17?

Find the highest floor an egg survives a drop, minimizing worst-case drops. You have 2 identical eggs; a broken egg is gone.

Pay a worker one-seventh of a gold bar each day for 7 days, cutting the bar only twice.

5 barrels of wine, exactly one poisoned; poison kills in exactly 24 hours. A feast is in 24 hours (results arrive exactly at the start). What is the minimum number of people needed to taste and identify the poisoned barrel by feast time?

Student n toggles every nth locker (student 1 all, student 2 every 2nd…). After 100 students, which lockers are open?

Three ants sit at a triangle's corners; each randomly picks a direction along an edge. Probability no collision?

Ants walk at 1 cm/s on a 1-metre stick; when two meet they reverse direction; falling off an end ends them. Max time until the stick is empty?

How many people are needed so that two share a birthday with probability > 50%?

A revolver has 6 chambers, 2 adjacent bullets. The cylinder spins once; the trigger is pulled repeatedly without re-spinning. You must shoot. Which turn do you choose?

Three colleagues want the average of their salaries; none wants anyone to learn their individual salary. How?

Candle A burns out in exactly 60 min, candle B in 45 min, both unevenly. Starting together, measure when exactly 15 minutes remain of a task window.

In 12 hours, how many times do a clock's hour and minute hands overlap?

A farmer must ferry a lion, a goat and a bundle of grass across a river. The boat carries the farmer plus one item. Left alone: lion eats goat, goat eats grass. Minimum trips?

10 stacks of 10 coins; one stack's coins weigh 9g instead of 10g. You have a digital scale and may weigh ONCE. Find the bad stack.

Measure 15 minutes using a 7-minute and an 11-minute hourglass, starting to cook immediately.

Three switches downstairs, three lamps upstairs, one trip upstairs. Match every switch to its lamp.

100 islanders, any who can deduce their own eye colour leaves that night; none can communicate, all see everyone's eyes; at least one has blue eyes. An outsider announces 'at least one of you has blue eyes.' What happens?

Two trains 100 km apart approach at 50 km/h each. A fly at 75 km/h shuttles between them. How far does the fly travel before they meet?

Blindfolded with a shuffled deck (26 red, 26 black). Split it into two piles with the same number of red cards each. How?