# day/dydd 208 at 7puzzleblog.com

T he Main Challenge

This puzzle invites you to use seven 2’s (2 2 2 2 2 2 and 2), with + – × ÷ available, in each separate calculation.

For instance, to make 1 and 2 you could simply do:

•  2 + (2÷2)  (2÷2)  (2÷2)  =  1
•  2 + 2 + 2 + 2  2  2  2  =  2

Can you show how to make 3, 4, and 5 when using seven 2’s?

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 2nd & 5th rows of the playing board contain the following fourteen numbers:

6   7   8   16   17   21   28   48   50   55   63   64   81   84

Which four numbers, when 2 is added to them, each become multiples of 5?

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 FIVE different ways to make 208 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?

1    4    9    16    25    36    49    64    81    100

#SquareNumbers

The Target Challenge

Can you arrive at 208 by inserting 45and 8 into the gaps on each line?

•  (◯×◯+◯)×◯ = 208
•  (◯×◯–◯)×◯ = 208
•  ◯³–◯×(◯–◯) = 208
•  (◯+◯)×(◯+double◯) = 208

Answers can be found here.

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