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.

As Easy as 1,2,3

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type 'TWO' it returns 2, and so on.

Sum Equals Product

Age 11 to 14 Challenge Level:

Here are some examples you could try:

$4 + 1 \frac{1}{4}$ and $4 \times 1 \frac{1}{4}$

$5 + 1 \frac{1}{4}$ and $5 \times 1 \frac{1}{4}$

$5 + 1 \frac{1}{5}$ and $5 \times 1 \frac{1}{5}$

$6 + 1 \frac{1}{5}$ and $6 \times 1 \frac{1}{5}$

Which of these give the same answer for both calculations?
Can you use these examples to help you find some more pairs that have the same sum and product?