# day/dydd 101 at 7puzzleblog.com

T he Main Challenge

Using each of the numbers 0.5, 1, 1.5 and 2 once each, with the four arithmetical operations – × ÷ available, can you arrive at the target answer of 7?

For the number puzzle enthusiast, can you find a 2nd way of making 7?

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 contain the following fourteen numbers:

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

Which THREE numbers, when 19 is added to each of them, become square numbers?

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 ways of making 101 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 57 and 10 once each, with + – × ÷ available, which 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 101 by inserting 5, 8, 10 and 11 into the gaps on each line?

•  ◯×◯–(◯–◯)² = 101
•  (+◯)×◯+ = 101
•  ◯×+◯+double = 101

Answers can be found here.

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