Some years ago, at a nice dinner with some geeks after a programming contest, somebody presented to me the following problem: Given the numbers 1, 3, 4 and 6, find an expression that yields 24. The expression can use addition, subtraction, multiplication, division, parentheses as much as you want. You have to use all the numbers exactly once. Don’t concatenate them: 1, 3 is not 13… As an example, 4 * (6 — 1) + 3 would be a valid expression. The only bad thing about that one is that it’s result is only 23, one short of 24. Can you find a better one?

Brain training is at the moment very popular in my family, mostly due to a Pocket PC game called SPB Brain Evolution. So this should come as a welcome challenge, shouldn’t it? But programmer’s are lazy, people say. Instead of shuffling around numbers and operators for hours, why not write a program to do the task? (The fact that writing a program for this problem might take a couple of hours, too, is happily ignored ;-)) This I did, and as a bonus, it came up with a handful other nice problems. If you want to take your quest for the number 24 a bit further, why not use 1, 6, 7 and 9 to compute it? Or 2, 5, 7 and 8? What about 2, 7, 8, 9? In each case, there is exactly one way to reach 24¹.

But maybe 24 is too high a number and makes things overly complicated. Why don’t we try to obtain one instead? Using 1, 4, 6, 7 it should give you something to do during a boring lecture ;-)

Finally, you can download the sourcecode (in Python) if you’re interested in the solutions… or write a comment to this post to get a hint. Happy calculating!