This week the 1729 Maths School was featured in the Guardian’s ‘Can you solve it’ column, a biweekly feature containing fun maths problems.
Here are two of the puzzles.
The missing seventh
I have six strips of wood with lengths 1, 2, 7, 9, 17 and 29 centimetres. It is impossible to arrange any three of these strips into a triangle. I would like to add another strip of wood, no longer than 29cm, so that I still cannot take three strips and make a triangle.
How many different lengths are possible for the missing seventh strip, and what are they? Lengths must be a whole number of centimetres.
As a bonus, what shape can I make using only these hypothetical extra strips?
The missing sixth
I have four numbers, a, b, c, and d.
There are six ways to multiply two of these numbers together: ab, cd, ac, bd, ad, bc.
The values of five of these products (not necessarily in this order) are 2, 3, 4, 5 and 6.
What is the value of the missing sixth product?