# day/dydd 70 at 7puzzleblog.com T he Main Challenge

Using the numbers 1, 4 and 6 once each with + – × ÷ available, list the SIX numbers that are mathematically possible to make in the range 20 to 30 inclusive. 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 & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

What is the sum of the factors of 100 listed above? 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 70 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 46 and 12 once each, with + – × ÷ available, which TWO 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 70 by inserting 2, 5, 6 and 10 into the gaps on each line?

•  ◯×◯+◯× = 70
•  ◯×◯+◯×◯² = 70
•  (◯+◯)×–double◯ = 70   