# day/dydd 50 at 7puzzleblog.com

T he Main Challenge

Using the numbers 4, 5 and 6 once each, together with + – × ÷, which THREE target numbers from the following list are NOT mathematically possible to make?

2    3    4    5    6    7    10    12    14    15    19    20    26    29    30

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 3rd & 7th rows contain the following fourteen numbers:

4   11   13   24   25   27   30   36   42   45   66   70   77   80

What is the difference between the highest and lowest multiples of 7?

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 50 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 89 and 10 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 50 by inserting 2, 5, 10 and 20 into the gaps on each line?

•  ²–◯×◯÷ = 50
•  (+)×◯+◯ = 50
•  ◯⁵+◯–◯÷◯ = 50