# day/dydd 87 at 7puzzleblog.com T he Main Challenge

Which is the ONLY way to make 38 when adding together SIX unique digits from 1-9? 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

Which number, when 5 is added to it, becomes a square number? 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 87 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?

1    4    9    16    25    36    49    64    81    100

#SquareNumbers

The Target Challenge

Can you arrive at 87 by inserting 3, 4, 6 and 7 into the gaps on each line?

•  ◯×◯×√◯+◯ = 87
•  ◯²×(◯+◯)–double◯ = 87
•  (◯+◯)²+double(◯–◯) = 87   