# DAY/DYDD 172: T he Main Challenge

You are playing our Mathematically Possible board game and have rolled the numbers 6, 6 and 6 with your three dice.  Using these once each, with + – × ÷ available, which SIX target numbers from 1-30 is it possible to make? 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 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

What is the difference between the sum of the multiples of 7 and the sum of the multiples of 9? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 172, in EIGHT different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which are the SIX target numbers it’s 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 172 by inserting 3, 4, 5 and 8 into the gaps on each line?

•  (◯+◯×◯)×◯ = 172
•  (◯+◯)²+◯²+◯ = 172   