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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.

The Cantor Set

Age 11 to 14
Challenge 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.