# day/dydd 131 at 7puzzleblog.com T he Main Challenge

Can you insert the numbers 0 to 9 exactly TWICE each into the gaps below so all five lines work out arithmetically?

◯  +  ◯   =    15    =   ◯  +  ◯
◯  +  ◯   =     5     =   ◯  –  ◯
◯  +  ◯   =    10    =   ◯  ×  ◯
◯  –  ◯   =     2     =   ◯  ÷  ◯
◯  +  ◯   =     9     =   ◯  ×  ◯

If you enjoyed attempting this, click this Mathelona link for details of our slightly easier pocket book challenges. 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 3rd & 6th rows contain the following fourteen numbers:

5   12   13   18   20   25   33   36   42   45   49   56   66   80

What is the sum of the numbers in the 40’s? 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 131 when using Lagrange’s Theorem. Can you find them all? The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?

6    12    18    24    30    36    42    48    54    60

#6TimesTable

The Target Challenge

Can you arrive at 131 by inserting 4, 5, 7 and 9 into the gaps on each line?

•  ◯×◯×◯–◯ = 131
•  ◯×◯×√◯+◯ = 131   