# day/dydd 204 at 7puzzleblog.com

Th e Main Challenge

Divide these nine numbers into three groups of three so that the sum of each group is the same:

11     25     35     43     51     63     73     85     91

What is this sum?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 1st & 3rd rows of the playing board contain the following fourteen numbers:

2   9   13   14   15   22   25   36   40   42   45   66   72   80

What is the difference between the 2nd highest even number and 2nd lowest odd 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 SEVEN different ways to make 204 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Using 57 and 11 once each, with + – × ÷ available, which are the only THREE numbers 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 204 by inserting 14and 10 into the gaps on each line?

•  (◯+◯×◯)×◯ = 204
•  double(◯²+◯+◯–◯) = 204
•  (◯³–treble◯)×(◯+◯) = 204

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