# day/dydd 45 at 7puzzleblog.com T he Main Challenge

If you multiply two whole numbers together and then add 4, the result is 40. Which one of the following could NOT be the sum of the two whole numbers you initially multiplied?

12      13      15      18      20      37 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 & 6th rows contain the following fourteen numbers:

5   8   12   17   18   20   28   33   48   49   55   56   63   64

Can you find four different numbers that 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 FOUR ways of making 45 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 89 and 10 once each, with + – × ÷ available, which is the ONLY number it is 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 45 by inserting 2, 3, 5 and 6 into the gaps on each line?

•  (◯×◯÷◯)× = 45
•  ◯²+◯×◯+ = 45
•  (◯+◯)×◯+◯ = 45   