Is it an interesting question?

Problem: Can you arrange the numbers 1 to 17 in a row, so that each adjacent pair adds up to a square number?

This is Sticky Numbers from NRICH. 

I shared it in a conference session that I was running, gave people number cards and asked them to try it in groups. When they were sure they had a solution I asked them to find other numbers, n, such that the set of numbers 1 - n  could be arranged so that each adjacent pair added up to a square number. 

I knew it was possible for other n as I had seen this beautiful gif on Mathani's tumblr.

After a while I set up a conjectures board for the ideas that were being suggested and a list of n for which the chain is possible.

There were a few things I noticed.

  • there was a sense of achievement having completed the first task where n = 17
  • people spontaneously came up with their own conjectures
  • people were invested in working on their own conjectures

It was also interesting to look at the range of recording strategies that occurred.

I wonder what was it about this problem that made it interesting enough for people to work on it for so long?