# day/dydd 75 at 7puzzleblog.com T he Main Challenge

2   +5   ÷2   ×5   4   ÷9   +1   ×5   1   ÷4   =   ? The 7puzzle Challenge

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

The 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

Which four different numbers, when added together, have a total 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 FIVE ways of making 75 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 46 and 12 once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

1    4    9    16    25    36    49    64    81    100

#SquareNumbers

The Target Challenge

Can you arrive at 75 by inserting 3, 4, 5 and 10 into the gaps on each line?

•  (◯+◯)×◯+◯ = 75
•  ◯²×(◯–◯–◯) = 75
•  ◯×◯+◯²+◯² = 75   