Est. 1998 — 27 years of woodworking knowledge
Early Friday Puzzler -- square sums
Alex Y
I'm going to be out of pocket tomorrpw, so here's an early one.
List the numbers one through 17 such that each pair of adjacent numbers adds to a perfect square. e.g., 3,1,8 could appear in the list, since 3+1 = 4 = 2^2 and 1+8 = 9 = 3^2. (The list has 16 pairs -- it does not "wrap around", so the first and last do not need to add to a perfect square.)
Re: Early Friday Puzzler -- square sums
Larry Barrett
I found one sequence, I wonder if there are others. My sequence of squares can be represented this way: c a b c b a b c b a b c b a b c.
Re: Early Friday Puzzler -- square sums
Alex Y
I'm not sure I understand your representation. I thought I did, but can't match it. I believe there are only two answers, one being the reverse of the other.
Thinking I understood your representation, I came up with:
D C B A D C B A B C B A B C
Re: Early Friday Puzzler -- square sums
Larry Barrett
My 'representation' is the sequential list of the 16 squares that result from adding sequential pairs of numbers. My actual sequence starts with 17.
I can guess at what D C B and A stand for in your representation but your list contains only 14 letters. Aren't there are supposed to be 16?
Correct!
Alex Y
And you'd think that by the time I reached my age I would have learned to check my work! What could be more basic and easier than to count the items in the list?!
Being more careful, I came up with a list that matches yours (actually the reverse) with your representation of squares. And I still believe that this is the only solution (considering reversing the list to be too trivial to count as a second solution).