Minimal InformationDifficulty 66 questionsby Marco DeLuca
Puzzles about extracting the maximum insight from the minimum data. How few tests, measurements, or observations do you need to guarantee a result?
Instructions
Each puzzle is about strategy and information efficiency. Explain your approach and why it guarantees the answer in the fewest steps. Show your reasoning for full credit.
Question 1 of 6
A prisoner must identify one of two pills. One pill is harmless and the other is fatal. He knows a glass of water beside them is poisoned, but he can survive by taking the harmless pill without the water. Yet the prisoner takes the harmless pill with the water and dies. What killed him?
A man says, "I know exactly what your two-digit number is." His friend replies, "Impossible — I only told you that the digits add to 9." How could the man still know the number? Or can he?
You have two ropes. Each rope takes exactly one hour to burn from end to end, but they do not burn at a constant rate — some sections burn faster than others. How can you measure exactly 45 minutes?
There are 100 doors in a row, all initially closed. You make 100 passes. On pass 1 you toggle every door, on pass 2 every 2nd door, on pass 3 every 3rd door, and so on until pass 100. Which doors remain open at the end?
You have 12 marbles that look identical, but one is heavier than the rest. You have a balance scale and may use it only three times. What is the optimal first move, and why?
You need to find the highest floor of a 100-floor building from which an egg can be dropped without breaking. You have only 2 identical eggs. What strategy minimizes the worst-case number of drops, and what is that number?