# DAY/DYDD/GIORNO/NAP 36: T he Main Challenge

You’ve rolled the numbers 2, 3 and 4 with three dice.  Using these once each, with + – × ÷ available, what is the lowest positive whole number it is NOT possible to make? 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 1st & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

Which three different numbers have a sum of 100? 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 36 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 26 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 36 by inserting 2, 3, 4 and 6 into the gaps on each line?

•  (◯+◯+◯)× = 36
•  (◯²+◯)×◯÷ = 36
•  (◯–◯)×◯× = 36
•  ◯²×(◯+◯–◯) = 36  (2 different ways)   