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Tweedle Dum and Tweedle Dee

Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM...

Special Sums and Products

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.


Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

Sum Equals Product

Age 11 to 14 Challenge Level:

I have been practising arithmetic with fractions.

I worked out $4 + 1 \frac{1}{3}$ but then realised that I had misread the question!

I was supposed to work out $4 \times 1 \frac{1}{3}$

When I worked out the multiplication, I was surprised to find I got the same answer to both calculations!

Can you find other examples of calculations where replacing the multiplication sign by an addition sign does not alter the result of the calculation?