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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... ### Sum Equals Product

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 ï¿½ 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers? ### 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.

# Peaches Today, Peaches Tomorrow...

##### Age 11 to 14Challenge Level

The monkey will always keep a whole number of peaches.

For part (ii), you could use a tree diagram: at each stage, branch off the fractions it would be possible to try next so that all possibilities are checked.

For Part (iii), why not try a starting value and see what happens? Then decide whether you need to start with a bigger or smaller starting value next time.