Posted by: Alexandre Borovik | February 8, 2015

Soldiers and horses

From a discussion at a LinkedIn group on mathematics education:

Q: You’re the general of an army. You have many soldiers and many horses. Each soldier needs one horse. What’s the fastest, most efficient way to see if the # of soldiers = the # of horses?

A: Tell the soldiers that the war is over, and  that they can go home, and take one horse each.

There is an interesting class of mathematical problems: intentionally ambiguous, because the rules of the game (or criteria for correctness of the answer) are not set;  a solution should, first of, recover – or set –  the rules, and set in a way that makes it immediately obvious that this is the only sensible set of rules, and the only sensible answer.

I do not know what were the intentions of the person who asked this question, but the answer perfectly fits into this humorous (or comical) side of mathematics.

Breaking the rules (or a  clash between two interpretation of the rule, or finding a consistent set of rules that fit into the problem better than an inspected answer) is the essence of many situation which perceived by humans as comical.

This is the rarely discussed  “comical” aspect of mathematics.


  1. i alwasys like the pigeonhole principle (where i grew up we had a whole roost of them plus wild cats, raccons, possums, rats, etc.) another one is the n-student random assignment number’—suppose you have n students and each is required to select a unique number for identification, with absiolutely no information about what numbers others are selecting, and of course no communication. thisd is one of those MIRI/lesswrong’/superintellgience (machines rule the world) kind of problems, but it may be ill posed.

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