# day/dydd 82 at 7puzzleblog.com T he Main Challenge

Using each of the four numbers 0.8, 0.9, 1.5 and 5 once each, and with the four arithmetical operations + – × ÷ available to use, can you arrive at the target answer of 7? 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 2nd & 3rd rows contain the following fourteen numbers:

8   13   17   25   28   36   42   45   48   55   63   64   66   80

What is the sum of the prime numbers? 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 82 when using Lagrange’s Theorem. Can you find them all? The Mathematically Possible Challenge

Using 23 and 11 once each, with + – × ÷ available, which THREE numbers are possible to make from the list below?

7    14    21    28    35    42    49    56    63    70

#7TimesTable

The Target Challenge

Can you arrive at 82 by inserting 1, 8, 9 and 10 into the gaps on each line?

•  ◯×◯–◯× = 82
•  ◯²+◯+◯–◯ = 82
•  ◯×◯+√◯–√ = 82
•  ◯×◯×◯+ = 82   