# day/dydd 30 at 7puzzleblog.com The Main Challenge

When listing the first seven whole numbers, above 20, that are not multiples of 3, 5 or 7 or do not contain a 3, 5 or 7 as part of their number, what is the 7th number in your list? 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 & 6th rows contain the following fourteen numbers:

5   12   13   18   20   25   33   36   42   45   49   56   66   80

Can you find FIVE groups of three different numbers that each total 99? 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 TWO ways of making 30 when using Lagrange’s Theorem. Can you find them both? The Mathematically Possible Challenge

Using 26 and 11 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 30 by inserting 2, 3, 5 and 10 into the gaps on each line?

•  ◯²+◯–(◯+◯) = 30
•  ◯×√(◯×◯×◯) = 30
•  (◯²+◯)×◯÷◯ = 30   