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Look at the following row of numbers:

\[10\quad 15\quad 21\quad 4\quad 5\]


They are arranged so that each pair of adjacent numbers adds up to a square number:

\[
10 + 15 = 25
\]
\[
15 + 21 = 36
\]
\[
21 + 4 = 25
\]
\[
4 + 5 = 9
\]

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


This printable set of cards, or the number cards in the interactivity below, might help you to test different options.

Can you arrange them in more than one way? If not, can you justify that your solution is unique?



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Printable NRICH Roadshow resource.