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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.