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.