- 02 Jul '04 01:44See how many integers you can form, starting with 1 and going through 10, by using only the digit 4 four times - no more, no less - and the multiplication, division, addition and/or subtraction signs.

Samples:

1 = 44/44

2 = 4/4 + 4/4

By adding the square-root sign, 11 through 18 are readily obtainable. So start with 3 and see how far you can go.

-Ray. - 02 Jul '04 16:48 / 2 edits19 = 4! - (4 + 4/4)

20 = 4! - 4 + 4 - 4

21 = 4! -4 + 4/4

22 = 4! - sqrt(4) + 4 - 4

23 = 4! - sqrt(4) + 4/4

24 = 4*4 + 4 + 4

25 = 4! + sqrt(4) - 4/4

26 = 4! + sqrt(4) + 4 - 4

27 = 4! + 4 - 4/4

28 = 4! +4 - 4 + 4

29 = 4! + 4 + 4/4

30 = 4! + sqrt(4) + sqrt(4) + sqrt(4)

and not sure this is optimal, but...

31 = 4! + 4/(.4 recurring) - sqrt(4)

EDIT

better is:

31 = 4!+ (4! + 4)/4 - 04 Jul '04 08:44

Are also standard functions acceptable? Is it valid if I define ONE(x) as a function such that ONE(4) = 1, that could be defined with standard functions as:*Originally posted by rgoudie***I think that after passing 30, all mathematical symbols are acceptable.**

floor(cubic root(x)) or

ceil(log(x)) or

sign(x)

This way,

32 = (4+4) x sqrt(4x4)

33 = 4! + 4 + 4 + ONE(4)

34 = 4! + 4 + 4 + sqrt(4)

35 = 4! + (4! / sqrt (4)) - ONE(4)

36 = 4^4 - 4! - 4

-- Germano - 05 Jul '04 10:29

it's only a way to say one of the other (valid, as you confirmed) three... just substitute it with ceil (log(4)), this is the sense. Anyways, 36 was wrong, it's quite easily*Originally posted by rgoudie***I'm not too sure about that [b]one**function.

-Ray.

[/b]

36 = (4+4)x4 + 4

while 37... I really can't figure it! 8-)