01-18-2018, 09:32 PM
Some of you may have seen the numberphile video about the "sum of squares" problem.
The problem is simple.
One has the following sequence:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
The objective is to rearrange them in a way that every two adjacent numbers, if added, are equal to a square of an integer number. The problem is to use all the numbers.
Example 1,3,6,10,15 (it fails then)
Don't read below if you want to give it a try.
then in the video they said they tested all the sequences up to 299. From 25 to 299 they found a way and likely there will be always a way.
The point is, using only real calculators (surely someone already run some programs until one million on some pc/tablet/smartphone), could we break 299 ?
I guess the 50g, prime, dm42 have good chances to break 299 if programmed in a clever way, given enough time.
The problem is simple.
One has the following sequence:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
The objective is to rearrange them in a way that every two adjacent numbers, if added, are equal to a square of an integer number. The problem is to use all the numbers.
Example 1,3,6,10,15 (it fails then)
Don't read below if you want to give it a try.
Code:
SPOILER:
I personally solved it when in the video they said "it is possible to solve it".
How a sentence can change the attitude towards a little problem.
I first listed all the possible working couples,
then I made a "clock" with the numbers and I started to connect them.
9,7,2,14,11,5,4,12,13,3,6,10,15,1,8
then in the video they said they tested all the sequences up to 299. From 25 to 299 they found a way and likely there will be always a way.
The point is, using only real calculators (surely someone already run some programs until one million on some pc/tablet/smartphone), could we break 299 ?
I guess the 50g, prime, dm42 have good chances to break 299 if programmed in a clever way, given enough time.