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'No Matter' printed from http://nrich.maths.org/
Think of a whole number, double it, then add 3. Multiply your answer by 4 and from this take away 5. Now also take away the number you first thought of.
No matter what your first number was, your answer will be a multiple of which number?
If you liked this problem, here is an NRICH task
which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.