# day/dydd 21 at 7puzzleblog.com The Main Challenge

Which is the lowest whole number that is NOT a multiple of 4, 5 or 6, nor a prime number, square number or cube number? 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

Which odd number, when 1 is subtracted from it, becomes a prime number? 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 21 when using Lagrange’s Theorem. Can you find both? The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which is the ONLY number it is 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 21 by inserting 3, 4, 5 and 6 into the gaps on each line?

•  (◯+◯–◯)×◯ = 21
•  ◯×◯+(◯+◯) = 21
•  ◯²–(◯×◯÷◯)² = 21   