Expressions(xxx)

Here is a problem by J.A.H. Hunter.

It's the 'expressions' game again today. Using three 'ones,' but with no other figures at all, make an expression for 24. With the three 'ones,' of course, you may use any mathematical signs you know; but no words, such as 'log.' For example, if you had to express the number 10 in this game, it could be (11-1). Then do the same with three 'twos.' After that with three 'threes,' and so on right up to three 'nines.'

Use SQRT for the square root, r for repeating decimal(.ar=.aaaa...), and ^ as the power symbol. They are all right as they are just a method to express mathematical signs. With the help of Andreas Gunnarsson's program I have managed to get all 9 cases. If you you know the answer to only some of the cases post it anyhow.

Peter Heichelheim

SPOILER

24 = (1+(1/sqrt(.1r)))! 24 = 2+22 24 = 3^3-3 24 = 4*(4+sqrt(4)) 24 = (5-(.5+.5))! 24 = 6*6*.6r 24 = (sqrt(7+7/.7r))! 24 = 8+8+8 24 = 9*sqrt(9)-sqrt(9)

Please reply to ilan at cedara dot com

Congratulations to all of you got the right answer.