Finding the pattern in this number sequence is hard, but all of your students from Year 7 to Year 13 can have a go at it. Starting from 1, the sequence has been constructed using all the numbers from 1 to 35 inclusive. Can you see what the pattern is?
The solution is very simple – each adjacent pair of numbers in the sequence sums to an exact square number.
To make the puzzle more challenging for older or brighter students, you can ask them to arrange the numbers from 1-35 in a sequence, so that every pair of adjacent numbers sums to a square number. You could start them off with 1, 3, 13, 23, … I don’t know if this is a unique solution.
The original source of the puzzle was A+Click, around 5 or 6 years ago. I can’t find this specific puzzle now, as there are currently more than 10,000 puzzles on the website. It has been growing since around 2010, and is aimed at students from grade 1 to grade 12 (age 5-17+). It currently lists contributors from 23 different countries, with most coming from the USA and the UK.