# day/dydd 47 at 7puzzleblog.com T he Main Challenge

If you multiply a certain number by 3 and then add 30, the result is the same as if you firstly added 17 to this particular number and then multiplied by 2.

Which number in the range 1 to 9 must this be? 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 & 7th rows contain the following fourteen numbers:

4   11   13   24   25   27   30   36   42   45   66   70   77   80

What is the product of the lowest number and highest number? 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 47 when using Lagrange’s Theorem. Can you find both? 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?

8    16    24    32    40    48    56    64    72    80

#8TimesTable

The Target Challenge

Can you arrive at 47 by inserting 2, 6, 7 and 10 into the gaps on each line?

•  ◯×◯+◯÷ = 47
•  ◯²(◯+◯)÷ = 47
•  (◯+◯)²–(+◯) = 47   