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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

You could try:
twist, twist, twist, turn, twist, twist, twist, turn, twist, twist, twist, turn, ... , twist, twist, twist, turn

Does it lead to special fractions?

If you are starting at 0 and trying to arrive at a particular fraction it may help to work backwards from the fraction you are wanting to reach.

If you've worked out a strategy for disentangling any tangled ropes you may have some insights that could help you do the opposite (ie. start at 0 and reach any fraction). See More Twisting and Turning