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Euler's Squares
Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...
DOTS Division
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
2-digit Square
A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?
Age 14 to 16 Challenge Level:
You may want to start by exploring how many hollow square arrangements there are for smaller battalions.
Perhaps look for hollow square arrangements of 48, 80, and 120 people.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.