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Patio

A square patio was tiled with square tiles all the same size. Some of the tiles were removed from the middle of the patio in order to make a square flower bed, but the number of the remaining tiles was still a square number. What were the dimensions of the patio and the flower bed?

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Time of Birth

A woman was born in a year that was a square number, lived a square number of years and died in a year that was also a square number. When was she born?

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Square Routes

How many four digit square numbers are composed of even numerals? What four digit square numbers can be reversed and become the square of another number?

Sticky Numbers

Stage: 3 Challenge Level: Challenge Level:1

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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