Friday, July 22, 2011

Four Fours Puzzle

A friend of mine was discussing a shopping centre on nearby Orchard Road which is sometimes known as the "Four Floors". I misheard him and assumed he was talking about the famous mathematical puzzle "Four Fours" first posed by WW Rouse Ball in his 1892 publication "Mathematical Recreations and Essays".

The challenge is to find
a mathematical expression for every integer from 0 and up using just the number 4, four times, with some basic mathematical operators. So, for example:

0 = 4 + 4 - 4 -4
1 = (4 + 4) / (4 + 4)
2 = (4 / 4) + (4 / 4)

and so on. In this case we won't allow 44 (forty-four) or .4 (four tenths), although some variations do. Amazingly people have found expressions for numbers well into the thousands.

See how many you can do and compare your ideas ours ideas!

1 comment:

  1. David Wheeler has answers for whole numbers up to 40,000 on his website http://www.dwheeler.com/fourfours/

    To do this he has to fall back on some "controversial" operators, such as %, the gamma function gamma(x) = (x-1)! and logical shifting ,as well as permit 0.4, 0.44 as well as 0.4 recurring (i.e. 4/9) and so on.

    Still, an impressive achievement!

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