## Elastic Numbers

It’s here! My new book of puzzles Elastic Numbers is now available on Amazon.

https://www.amazon.co.uk/Elastic-Numbers-Puzzles-Serious-Problem/dp/0995782601

https://www.amazon.com/gp/aw/d/0995782601

I hope you enjoy solving the problems as much as I enjoyed creating them.

## 42 Points

From the 2007 Australian Maths Competition:

There are 42 points $P_1, P_2, ..., P_{42}$ , placed in order on a straight line so that each distance from $P_i$ to $P_{i+1}$ is  $\dfrac{1}{i}$  for $1\leq i\leq 41$. What is the sum of the distances between every pair of these points?

## PuzzleCritic Originals: A strange festival

Here is a problem of my own invention; I hope you enjoy it:

At a festival, every guest presented a gift to every older guest. The ten youngest guests combined gave thirteen times as many gifts as they received. What was the total number of gifts presented at the festival?

## Subsets of subsets

From the 1992 Irish Maths Olympiad:

Let A be a nonempty set with n elements. Find the number of ways of choosing a pair of subsets (B,C) of A such that B is a nonempty subset of C.