# day/dydd 205 at 7puzzleblog.com

Th e Main Challenge

Pair the ten numbers below so that the difference between the two numbers in each pair is exactly divisible by 7:

6    17    28    37    45    58    64    78    83    98

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 sum of the factors of 80 listed above?

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 NINE different ways to make 205 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 TWO numbers it is possible to make from the list below?

10    20    30    40    50    60    70    80    90    100

#10TimesTable

The Target Challenge

Can you arrive at 205 by inserting 21011 and 15 into the gaps on each line?

•  (◯××◯)–◯ = 205
•  (◯+◯÷◯)×◯ = 205

Answers can be found here.

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