# day/dydd 127 at 7puzzleblog.com T he Main Challenge

With the four arithmetical operations + – × ÷ available, use all four numbers 1, 1.5, 2 and 6 once each in your attempt to make the target answer of 7. 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 2nd & 4th rows contain the following fourteen numbers:

3   8   10   17   28   32   35   44   48   54   55   60   63   64

What is the sum of the factors of 64? 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 127 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 24 and 12 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

1    3    6    10    15    21    28    36    45    55

#TriangularNumbers

The Target Challenge

Can you arrive at 127 by inserting 4, 7, 8 and 10 into the gaps on each line?

•  (◯+◯)×◯+◯ = 127
•  ◯²+◯×◯–◯ = 127
•  ◯²+◯+◯+double◯ = 127   