# DAY 177: The Main Challenge

If you enjoy this, click Mathelona for further details of our number puzzles.

You must make all three lines work out arithmetically by inserting the twelve digits 0, 0, 1, 1, 2, 3, 3, 4, 5, 6, 6 and 7 into the gaps below:

◯  +  ◯   =    7    =   ◯  –  ◯
◯  +  ◯   =    5    =   ◯  ×  ◯
◯  +  ◯   =    6    =   ◯  ÷  ◯ 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

Which two numbers have a difference of 21? 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 177, in EIGHT different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 36 and 12 once each, with + – × ÷ available, which FOUR target numbers is it possible to make from the list below?

5    10    15    20    25    30    35    40    45    50

#5TimesTable The Target Challenge

Can you arrive at 177 by inserting 1, 7, 9 and 11 into the gaps on each line?

•  ◯×(◯+◯)+◯ = 177
•  ◯²+(◯–◯)×◯ = 177 Answers can be found here. Click Paul Godding for details of online maths tuition. This entry was posted in 7puzzleblog.com. Bookmark the permalink.

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