# DAY/DYDD/GIORNO/NAP 65: T he Main Challenge

You must arrive at the target number of 24 by using four unique numbers from 10-19 and with + – × ÷ available to use; one such example being (15×12÷18)+14 = 24.

Can you derive another 4-number combination to make 24? The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 2nd & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

How many cube numbers are present? 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 65 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which FIVE numbers is it possible to make from the list below?

40    41    42    43    44    45    46    47    48    49

#NumbersIn40s

The Target Challenge

Can you arrive at 65 by inserting 1, 5, 6 and 8 into the gaps on each line?

•  (◯+◯–◯)× = 65
•  ◯×◯+(◯–◯)² = 65
•  ◯²+(◯+◯)÷◯ = 65
•  ◯²+◯–◯×◯ = 65   