# day/dydd 33 at 7puzzleblog.com The Main Challenge

Using the three numbers 3, 6 and 9 just once each, with + – × ÷ available, THREE of the following target numbers are not possible to make:

3   6   9   12   15   18   21   24   27   30   33   36

What is the sum of these three impossible numbers? 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 5th & 7th rows contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

Which number on the list, when multiplied by 5, has its result also on the list? 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 THREE ways of making 33 when using Lagrange’s Theorem. Can you find them? 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?

9    18    27    36    45    54    63    72    81    90

#9TimesTable

The Target Challenge

Can you arrive at 33 by inserting 2, 3, 4 and 5 into the gaps on each line?

•  (◯++◯)× = 33
•  (◯+)×◯– = 33
•  (³+◯–◯)÷◯ = 33   