# day/dydd 81 at 7puzzleblog.com

ThMain Challenge

Carry out the following 15-step number trail – with no calculator!

+1  ÷3  ×5  –7  +2  ÷6  +4  –1  ×3  ÷4  +4  –5  ×1  +3  ×6  =  ?

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 & 3rd rows contain the following fourteen numbers:

8   13   17   25   28   36   42   45   48   55   63   64   66   80

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 SIX ways of making 81 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 23 and 11 once each, with + – × ÷ available, which TWO numbers are possible to make from the list below?

6    12    18    24    30    36    42    48    54    60

#6TimesTable

The Target Challenge

Can you arrive at 81 by inserting 2, 3, 6 and 9 into the gaps on each line?

•  ◯×◯×◯÷ = 81
•  ◯²××◯÷◯ = 81
•  ◯²+×(+) = 81