# day/dydd 100 at 7puzzleblog.com T he Main Challenge

Starting from ONE, what is the 7th whole number, when written in English, that does NOT contain the letter ‘E’? The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 1st & 3rd rows contain the following fourteen numbers:

2   9   13   14   15   22   25   36   40   42   45   66   72   80

List THREE sets of four different numbers that all have a sum of 200, and THREE sets of three different numbers that all have a sum of 100. The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There are SEVEN ways of making 100 when using Lagrange’s Theorem. Can you find them all? The Mathematically Possible Challenge

Using 57 and 10 once each, with + – × ÷ available, which TWO numbers it is possible to make from the list below?

2    3    5    7    11    13    17    19    23    29

The Target Challenge

Can you arrive at 100 by inserting 4, 5, 8 and 10 into the gaps on each line?

•  ◯×◯+×◯ = 100
•  (+÷√◯)×◯ = 100
•  ◯²×(+) = 100
•  (³÷◯)×◯÷◯ = 100
•  ◯²×(+)² = 100
•  (×◯+)×√◯ = 100
•  ((×◯)÷(◯))² = 100   