# day/dydd 94 at 7puzzleblog.com T he Main Challenge

Using the numbers 3, 5 and 5 once each, with + – × ÷ available, which FOUR numbers from the following list are NOT mathematically possible to make?

1   2   3   4   7   10   13   15   18   20   22   25   28   30 The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 6th & 7th rows contain the following fourteen numbers:

4   5   11   12   18   20   24   27   30   33   49   56   70   77

What is the difference between the two prime numbers on the list? 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 FOUR ways of making 94 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 57 and 10 once each, with + – × ÷ available, which TWO numbers it is 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 94 by inserting 3, 5, 7 and 10 into the gaps on each line?

•  ◯³–◯×◯–◯= 94
•  ◯²–◯×(◯) = 94
• ◯²+◯×(◯+◯)= 94   (2 different ways) 