### 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...

### 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 =

### 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?

# Twisting and Turning

##### Stage: 3 Challenge Level:

Twisting has the effect of adding 1: $$x\rightarrow x + 1$$ Turning transforms any number into the negative of its reciprocal: $$x\rightarrow -\frac{1}{x}$$ Starting at zero, the first five moves: Twist, twist, twist, turn, twist
produces:$$0, 1, 2, 3, -\frac{1}{3}, \frac{2}{3}$$

Can you continue from there and then return to zero? You can use the reciprocal button on a calculator ($\frac{1}{x}$ ) to help with the calculations.

Take another look at the video. Can you spot the strategy they used to get back to 0?