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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?
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?
Age 11 to 14
Challenge Level
Sticky Numbers printable sheet (NRICH Roadshow resource)
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 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?
NRICH is part of the family of activities in the Millennium Mathematics Project.