Originally posted by MathurineI think I found a set which satisfies all but (4):
[b]Find a non-empty set of positive integers, base 10, no two equal, such that:
(1) For any number N in the set, none of the numbers in the set has N digits.
(2) For any number N in the set, the sum of the squares of the digits of N is also in the set.
(3) The number of numbers in the set is also in the set.
(4) The largest number in the set is equa ...[text shortened]... e with the fewest numbers, and among those,
find the one with the smallest largest number.[/b]
Originally posted by idiomsAny details on how you approached the problem? I tried a few different ways but got lost every time.
one of these numbers is kinda different, one of these numbers is not the same
i believe this is the smallest size set and top number that satisfies the criteria.
Originally posted by XanthosNZThis isn't going to be especially clear i'm afraid. It's hard to explain without mathematical notation
Any details on how you approached the problem? I tried a few different ways but got lost every time.
Originally posted by altfellcan't use 2
So.. I think I found the ultimate solution.
I started by the same algorithm as described before to see where does every number from 4 to 15 lead to.. it's no sense trying numbers greater than this, because the minimum set until this point had 16 numbers.
For 4 we have the most efficient set that solves rule nb 2.
So the minim ...[text shortened]... 580 which is the last number.
Originally posted by idiomsI think this is the set with smallest high number
This isn't going to be especially clear i'm afraid. It's hard to explain without mathematical notation
I knew the seed set i was looking for was self contained for not simply one iteration of the sum of squares algorithm but infinite iterations
I then wrote a perl program to sort all numbers of 4 digits or less into groups based on the number iterations umbers from other sets you can create a lower number but 16 is definitely minimum set size.