# day/dydd 51 at 7puzzleblog.com

T he Main Challenge

Using each of the numbers 0.1, 0.5, 3 and 6 once each, and with the four arithmetical operations available, can you arrive at the target answer of 7 in two different ways?

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 & 5th rows contain the following fourteen numbers:

2   6   7   9   14   15   16   21   22   40   50   72   81   84

Which three different numbers have a sum that is also on the list?

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 THREE ways of making 51 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 89 and 10 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

2    3    5    7    11    13    17    19    23    29

The Target Challenge

Can you arrive at 51 by inserting 4, 5, 6 and 7 into the gaps on each line?

•  (+)×◯+◯ = 51
•  ◯²+(◯+◯)÷ = 51
•  ◯×◯++◯ = 51
•  ◯×(◯+√◯)– = 51
•  ()²×+◯ = 51