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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 � 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.

# Racing Odds

##### Age 11 to 14 Challenge Level:

This is a nice solution from Andrei of School 205 Bucharest. Thank you Andrei.

Looking at the first race.

If the odds are 2 to 1 against the rhinoceros, then the probability that the rhinoceros will win is 1/(1 + 2) = 1/3. For the hippopotamus, the probability that he will win is 2/(2 + 3) = 2/5.

The total probability (that there is a winner) is 1. So, the probability that the elephant will win is:

1 -1/3 -2/5 = 4/15

So, the odds for him are 11 to 4 against the elephant.