# day/dydd 22 at 7puzzleblog.com The Main Challenge

… is a Kakuro-type puzzle.  As well as 9321 (or 9+3+2+1), there are FIVE other ways of combining and adding together four unique digits from 1-9 to make 15.  Can you list those five ways? The 7puzzle Challenge

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

The 2nd & 4th rows contain the following fourteen numbers:

3   8   10   17   28   32   35   44   48   54   55   60   63   64

What is the sum of the factors of 60? 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 TWO ways of making 22 when using Lagrange’s Theorem. Can you find both? The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which FOUR 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 22 by inserting 3, 4, 5 and 6 into the gaps on each line?

•  ◯×◯+◯÷◯ = 22
•  ◯×◯+◯–◯ = 22
•  ◯²+◯+◯+√◯ = 22   