### 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?

### 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?

### 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:

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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