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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...

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Lower Bound

What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =

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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?

All Tangled Up

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Oliver from Olchfa School suggests that if we work back to 0 (using -1 instead of +1 for the twists), and then reverse the sequence, we can arrive at any fraction we desire. Here is his explanation of how to proceed. Thank you Oliver.