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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}.
Novemberish
a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.
Age 14 to 16
Challenge Level
Take any two digit number, reverse its digits, and subtract the smaller number from the larger. For example $$42-24=18$$ I've tried this a few times and I never seem to end up with a prime number. Try some examples of your own. Do you ever end up with a prime number?
Can you prove that you will never end up with a prime?
What happens when I do the same with a three digit number?
What about a four digit number?
What about a five, six, seven, ... $n$ digit number?
Can you justify your findings?
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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.