# day/dydd 170 at 7puzzleblog.com T he Main Challenge

Study the seven clues and place the numbers 1-9 into the nine positions on this 3-by-3 grid. Each number should appear exactly once:

x              x              x

x              x              x

x              x              x

Clues:

1.  The 8 is directly above the 5,
2.  The 6 is further right than the 7,
3.  The 7 is further right than the 1,
4.  The 1 is lower than the 5,
5.  The 5 is further right than the 9,
6.  The 3 is higher than the 9 and further right than the 2,
7.  The 4 is higher than the 7 and further right than the 8. 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 & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

What is the difference between the sum of the highest and lowest even numbers and the product of the highest and lowest even numbers? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 170, in ELEVEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which is the ONLY target number it’s 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 170 by inserting 9, 10, 20 and 20 into the gaps on each line?

•  ◯+◯×◯–◯ = 170
•  (◯–◯÷◯)×◯ = 170   