# DAY/DYDD/GIORNO/NAP 32: The Main Challenge

Apart from 9+5+1, find the SEVEN other ways you can make 15 when combining and adding together three 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 up to 84.

The 5th & 7th rows contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

Which two pairs of numbers both have a difference of 11? 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 is just ONE way of making 32 when using Lagrange’s Theorem. Can you find it? The Mathematically Possible Challenge

Using 26 and 11 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

8    16    24    32    40    48    56    64    72    80

#8TimesTable

The Target Challenge

Can you arrive at 32 by inserting 2, 4, 7 and 8 into the gaps on each line?

•  ◯×+÷◯ = 32
•  ×÷◯+ = 32
•  (◯+◯)²÷◯+◯ = 32   