# day/dydd 31 at 7puzzleblog.com

The Main Challenge

Your task is to arrive at the target number of 20 by adding together five numbers.  You are limited to using digits 1 to 5 but these can be used any number of times in each calculation.

One way of making 20 is 4+4+4+4+4 (but you can write your answer as 44444 to save time). Can you list the other 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 5th & 7th rows contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

What is the sum of the 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 TWO ways of making 31 when using Lagrange’s Theorem. Can you find them both?

The Mathematically Possible Challenge

Using 26 and 11 once each, with + – × ÷ available, which THREE numbers is it 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 31 by inserting 1, 5, 6 and 6 into the gaps on each line?

•  ◯×× = 31
•  ◯²÷◯+²÷◯ = 31
•  (÷◯+◯)×◯ = 31

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