# day/dydd 162 at 7puzzleblog.com T he Main Challenge

Here’s a mini-Mathelona challenge where you must place the eight digits 0 1 1 2 2 2 3 and 4 into the eight gaps so both lines work out arithmetically:

◯  +  ◯   =    4    =   ◯  ×  ◯
◯  –  ◯   =    2    =   ◯  ÷  ◯

Click Mathelona for details of our pocket book challenges. 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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

Which two numbers, when each is divided by 6, also appear on the list? 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 (4+1+1+1).

Show how you can make 162, in THIRTEEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 35 and 8 once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

1     8     27     64     125

#CubeNumbers The Target Challenge

Can you arrive at 162 by inserting 239 and 12 into the gaps on each line?

•  ◯××(◯–◯) = 162
•  ◯³×(×◯–◯) = 162   