# day/dydd 86 at 7puzzleblog.com T he Main Challenge

How can you use six 7’s (7 7 7 7 7 and 7) once each, together with the four arithmetical operations + – × ÷, to arrive at the target answer of 100? 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 4th & 5th rows contain the following fourteen numbers:

3   6   7   10   16   21   32   35   44   50   54   60   81   84

What is the sum when adding together all the multiples of 10? 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 86 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 23 and 11 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

11    22    33    44    55    66    77    88    99    110

#11TimesTable

The Target Challenge

Can you arrive at 86 by inserting 2, 4, 10 and 14 into the gaps on each line?

•  ◯×(◯–◯)+◯ = 86
•  ◯×◯÷◯+² = 86
•  (◯²–◯)÷◯– = 86   