# DAY/DYDD 112: T he Main Challenge

If you multiply a mystery number by 6 and then subtract 6, the result is the same as if you first multiplied the same mystery number by 3 and then added 3.

Is the value of this mystery number 1, 2, 3, 4 or 5? 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 3rd & 4th rows contain the following fourteen numbers:

3   10   13   25   32   35   36   42   44   45   54   60   66   80

What is the sum of the multiples of 7 listed? 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 just THREE ways of making 112 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 14 and once each, with + – × ÷ available, which TWO 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 112 by inserting 3, 5, 10 and 11 into the gaps on both lines?

•  ◯×◯+◯ = 112
•  (◯+◯)×(◯◯) = 112   