Friday, May 7, 2010
For the mathematically inclined, here is something:
We have numbers from 0 to 100 written here, using at max 4 4's and some math operators. The operators that are used are, +, -, *, /, sqrt, . (decimal), ! (factorial) and ^ (to the power of).
However, I could not do some numbers, which are 73/77/87/93 and 99. Interested, please jump in.
(As an aside, is there some theory around these puzzles? I see these in my newspaper every day, and decided to compute these numbers).
4 - 4
4/4
sqrt(4)
sqrt(4) + 4/4
4
4 + 4/4
4 + sqrt(4)
4 + sqrt(4) + 4/4
4 + 4
4 + 4 + 4/4
4 + 4 + sqrt(4)
(4! - sqrt(4))/sqrt(4)
4!/sqrt(4)
(4! + sqrt(4))/sqrt(4)
(4! + 4)/sqrt(4)
4*4 - 4/4
4*4
4*4 + 4/4
4*4 + sqrt(4)
4! - 4 - 4/4
4! - 4
4! - 4 + 4/4
4! - sqrt(4)
4! - 4/4
4!
4! + 4/4
4! + sqrt(4)
4! + sqrt(4) + 4/4
4! + 4
4! + 4 + 4/4
4! + 4 + sqrt(4)
4! + (4! + 4)/4
4! + 4*sqrt(4)
4! + (4 - .4)/.4
4! + 4*sqrt(4) + sqrt(4)
4! + 44/4
4! + 4!/sqrt(4)
4! + (4! + sqrt(4))/sqrt(4)
44 - 4!/4
(4*4 - .4)/.4
44 - 4
(4*4 + .4)/.4
44 - sqrt(4)
44 - 4/4
44
44 + 4/4
44 + sqrt(4)
4!*sqrt(4) - 4/4
4!*sqrt(4)
4!*sqrt(4) + 4/4
4!*sqrt(4) + sqrt(4)
(4! - 4 + .4)/.4
4!*sqrt(4) + 4
(4! - sqrt(4))/.4 - sqrt(4)
(4! - 4)/.4 + 4
(4! - .4)/.4 - 4
4!/.4 - 4
(4! + .4)/.4 - 4
4!/.4 - sqrt(4)
(4! - .4)/.4
4!/.4
(4! + .4)/.4
4!/.4 + sqrt(4)
(4! + .4)/.4 + sqrt(4)
4!/.4 + 4
(4! + .4)/.4 + 4
(4! + 4)/.4 - 4
(4! + sqrt(4))/.4 + sqrt(4)
(4! + 4)/.4 - sqrt(4)
(4! + 4 - .4)/.4
(4! + 4)/.4
(4! + 4 + .4)/.4
(4! + 4)/.4 + sqrt(4)
73 not present
(4! + 4)/.4 + 4
(4! + 4 + sqrt(4))/.4
4!/.4 + 4*4
77 not present
4*(4! - 4) - sqrt(4)
(4! - sqrt(4))/.4 + 4!
(4! + 4 + 4)/.4
(4 - 4/4)^4
4!/.4 - sqrt(4) + 4!
(4! - .4)/.4 + 4!
4!/.4 + 4!
(4! + .4)/.4 + 4!
4!/.4 + sqrt(4) + 4!
87 not present
44*sqrt(4)
(4! + sqrt(4))/.4 + 4!
44*sqrt(4) + sqrt(4)
4!*4 - sqrt(4)/.4
4!*4 - 4
93 not present
(4! + 4)/.4 + 4!
4!*4 - 4/4
4!*4
4!*4 + 4/4
4!*4 + sqrt(4)
99 not present
4!*4 + 4
The scene from 101-200 is not that rosy. Many numbers can't be properly expressed here. That work is un-finished as of now. Will post it soon, as I conclude it.
We have numbers from 0 to 100 written here, using at max 4 4's and some math operators. The operators that are used are, +, -, *, /, sqrt, . (decimal), ! (factorial) and ^ (to the power of).
However, I could not do some numbers, which are 73/77/87/93 and 99. Interested, please jump in.
(As an aside, is there some theory around these puzzles? I see these in my newspaper every day, and decided to compute these numbers).
4 - 4
4/4
sqrt(4)
sqrt(4) + 4/4
4
4 + 4/4
4 + sqrt(4)
4 + sqrt(4) + 4/4
4 + 4
4 + 4 + 4/4
4 + 4 + sqrt(4)
(4! - sqrt(4))/sqrt(4)
4!/sqrt(4)
(4! + sqrt(4))/sqrt(4)
(4! + 4)/sqrt(4)
4*4 - 4/4
4*4
4*4 + 4/4
4*4 + sqrt(4)
4! - 4 - 4/4
4! - 4
4! - 4 + 4/4
4! - sqrt(4)
4! - 4/4
4!
4! + 4/4
4! + sqrt(4)
4! + sqrt(4) + 4/4
4! + 4
4! + 4 + 4/4
4! + 4 + sqrt(4)
4! + (4! + 4)/4
4! + 4*sqrt(4)
4! + (4 - .4)/.4
4! + 4*sqrt(4) + sqrt(4)
4! + 44/4
4! + 4!/sqrt(4)
4! + (4! + sqrt(4))/sqrt(4)
44 - 4!/4
(4*4 - .4)/.4
44 - 4
(4*4 + .4)/.4
44 - sqrt(4)
44 - 4/4
44
44 + 4/4
44 + sqrt(4)
4!*sqrt(4) - 4/4
4!*sqrt(4)
4!*sqrt(4) + 4/4
4!*sqrt(4) + sqrt(4)
(4! - 4 + .4)/.4
4!*sqrt(4) + 4
(4! - sqrt(4))/.4 - sqrt(4)
(4! - 4)/.4 + 4
(4! - .4)/.4 - 4
4!/.4 - 4
(4! + .4)/.4 - 4
4!/.4 - sqrt(4)
(4! - .4)/.4
4!/.4
(4! + .4)/.4
4!/.4 + sqrt(4)
(4! + .4)/.4 + sqrt(4)
4!/.4 + 4
(4! + .4)/.4 + 4
(4! + 4)/.4 - 4
(4! + sqrt(4))/.4 + sqrt(4)
(4! + 4)/.4 - sqrt(4)
(4! + 4 - .4)/.4
(4! + 4)/.4
(4! + 4 + .4)/.4
(4! + 4)/.4 + sqrt(4)
73 not present
(4! + 4)/.4 + 4
(4! + 4 + sqrt(4))/.4
4!/.4 + 4*4
77 not present
4*(4! - 4) - sqrt(4)
(4! - sqrt(4))/.4 + 4!
(4! + 4 + 4)/.4
(4 - 4/4)^4
4!/.4 - sqrt(4) + 4!
(4! - .4)/.4 + 4!
4!/.4 + 4!
(4! + .4)/.4 + 4!
4!/.4 + sqrt(4) + 4!
87 not present
44*sqrt(4)
(4! + sqrt(4))/.4 + 4!
44*sqrt(4) + sqrt(4)
4!*4 - sqrt(4)/.4
4!*4 - 4
93 not present
(4! + 4)/.4 + 4!
4!*4 - 4/4
4!*4
4!*4 + 4/4
4!*4 + sqrt(4)
99 not present
4!*4 + 4
The scene from 101-200 is not that rosy. Many numbers can't be properly expressed here. That work is un-finished as of now. Will post it soon, as I conclude it.
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