# day/dydd 132 at 7puzzleblog.com

T he Main Challenge

The 15 arithmetical steps below include percentage & fraction calculations as well as big additions & multiplications:

•  subtract seventy-five percent
•  +69
•  –4
•  1/2 of this
•  square root of this
•  ×15
•  multiply by one
•  +80%
•  –10
•  add four hundred and sixty-five
•  subtract three hundred and seventeen
•  two-thirds of this
• ×0.5
•  increase by 10%
•  decrease by 10%

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 3rd & 6th rows contain the following fourteen numbers:

5   12   13   18   20   25   33   36   42   45   49   56   66   80

Which of these numbers, when 65 is added to it, becomes a square 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 ways of making 132 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

7    14    21    28    35    42    49    56    63    70

#7TimesTable

The Target Challenge

Can you arrive at 132 by inserting 4, 5, 6 and 8 into the gaps on each line?

•  (◯+◯)×(◯+◯) = 132
•  (◯×◯–double◯)×◯ = 132