Thursday, June 7, 2012

3 3 7 7

Here's a fun puzzle (thank you Piotr!):

Using only multiplication, addition, subtraction, division, and parentheses, combine all of the four numbers 3, 3, 7, and 7 to get 24.

Apparently this is an example of the "24" game in which you do this with any other four numbers. (A related game I remember from middle school is to use the four digits of the current year to make as many numbers from 1 to 100 as possible, using more creative operations like !, mod, and exponentiation. This worked better in the 90s :)

This is a fun one in particular because it's really hard to figure out in your head, but when you use pencil and paper to explore more systematically, the two double numbers cuts down the number of possibilities drastically and it's very doable.


Now don't keep reading until you figure it out!


The answer is to use fractions in the intermediate values in an unobvious way. Three sevenths plus three is twenty four sevenths. And there you go. (I spelled that out in words intentionally because you can't glance at it accidentally and give away the answer to yourself.)