# DAY/DYDD/GIORNO/NAP 177: T he Main Challenge

You must try and 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:

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

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

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   