Did you decide what to do about the milk in the coffee? If you answered “I take my coffee black” then I guess that counts as lateral thinking and should get some credit. Martin Gardener’s advice was to add the milk straight away, so he clearly liked milk in his coffee and he knew what he was doing! The reason is that the rate of cooling depends on the temperature you start at, or in mathematical terms there is a differential equation , where denotes the temperature of the coffee and k is a negative constant governing the rate of cooling..
Of course dumping a jug of milk into the coffee with immediately cool it further, with the result depending on the relative quantities of milk and coffee and the difference in the temperature. It will effectively average out the difference. That means the effect of dumping in the milk to start with is to lower the starting temperature and reduce the rate of cooling, whereas waiting allows the coffee to cool faster and the effect of adding the milk further reduces the temperature.
If you are not entirely convinced by this you will need to learn enough calculus to understand the differential equation above and to solve it!
Now for another classic puzzle: Imagine there are 100 top-ranked gamers in a huge online tournament who just won a prize of 10,000 game coins. These gamers are ranked by skill from best (ranked #1) to lowest (ranked #100). They need to decide how to split the prize.
Here’s how it works: the top-ranked gamer (gamer #1) gets to propose a plan for dividing the coins. This plan could be anything, like “I get all the coins” or “Everyone gets an equal share.” After making a plan, all 100 gamers vote on it. If 50% or more agree with the plan, it’s accepted, and that’s how the coins are divided. But if more than 50% vote against it, the gamer who made the plan is disqualified from the tournament (basically, kicked out of the game). Then the next gamer in line (gamer #2) gets to make a plan, and the voting rules start over.
One key detail: each gamer is perfectly logical. They’ll always think through the situation to try to stay in the game and maximize the coins they receive.
Now, as the top-ranked gamer (gamer #1), how can you get the most coins for yourself without being voted out? How would you do it?