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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 ï¿½ 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.

# The Cantor Set

##### Age 11 to 14Challenge Level

Liam from Wilbarston School sent us this well-explained solution:

Only the middle thirds of line segments are removed, so endpoints of line segments will not be removed.
Therefore, all I need to do is determine which are endpoints and which are not.

$\frac{1}{3}$ is an endpoint of C2, so it is in the Cantor set.

$\frac{3}{81}$ = $\frac{1}{27}$

$\frac{1}{27}$ is an endpoint of C4, and therefore $\frac{3}{81}$ is in the Cantor set.

$\frac{4}{9}$ is between $\frac{1}{3}$ and $\frac{2}{3}$, thus it is in the middle third of C1 and is removed from C2 and as such isn't in the Cantor set.

$\frac{4}{81}$ is between $\frac{1}{27}$ and $\frac{2}{27}$ and therefore is in the middle third of C3.
It is removed from C4 and therefore does not belong.