# day/dydd 215 at 7puzzleblog.com

T he Main Challenge

By using the four numbers 0.5, 2, 2 and 2 exactly once each, can you arrive at the target answer of 7 with the four arithmetical operations + – × ÷ available to use?

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 1st & 2nd rows of the playing board contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

From the list, find the sum of the multiples of 7.

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 215 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Using 46 and once each, with + – × ÷ available, which are the SIX numbers it is possible to make from the list below?

6    12    18    24    30    36    42    48    54    60

#6TimesTable

The Target Challenge

Can you arrive at 215 by inserting 4, 15, 20 and 40 into the gaps on each line?

•  ◯×◯+◯+double◯ = 215
•  (◯×◯)÷◯+◯ = 215
•  quarter(◯×◯+◯×◯) = 215

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