# day/dydd 179 at 7puzzleblog.com

T he Main Challenge

You must make all three lines work out arithmetically by inserting the twelve digits 0 1 1 2 2 3 4 4 5 6 8 and 8 into the gaps below:

◯  +  ◯   =    6    =   ◯  –  ◯
◯  +  ◯   =    8    =   ◯  ×  ◯
◯  +  ◯   =    2    =   ◯  ÷  ◯

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The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

List two sets of three different numbers that both have a total of 77.

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 179, in SIX different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 36 and 12 once each, with + – × ÷ available, which THREE target 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 179 by inserting 5, 6, 7 and 22 into the gaps on each line?

•  (◯+◯)×◯+◯ = 179
•  (half◯)²+10×◯+◯–◯ = 179