See 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.
- Joined
- 26 Apr 03
- Moves
- 26771
2 edits
19 = 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
Originally posted by rgoudieAre 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:
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
Originally posted by rgoudieit'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
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-)