# DAY/DYDD 232: T he Main Challenge

Try the following Mathelona challenge, taken from our pocket book of challenges.

Can you make all three lines work out arithmetically by placing the 12 digits below into the 12 gaps?

0     1     1     2     2     3     3     4     5     6     6     7

◯  +  ◯   =    6    =   ◯  –  ◯
◯  +  ◯   =    9    =   ◯  ×  ◯
◯  +  ◯   =    3    =   ◯  ÷  ◯ 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 of the playing board contain the following fourteen numbers:

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

From the list, how many multiples of 9 are there? 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 different ways to make 232 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 24 and once each, with + – × ÷ available, which are the FOUR numbers it is 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 232 by inserting 4, 8, 12, 16 and 20 into the gaps below?

•  ◯×◯–◯×◯÷◯ = 232   