# day/dydd 210 at 7puzzleblog.com T he Main Challenge

Try the following Mathelona challenge, similar to my pocket book challenges but slightly tougher!

Your task is to make all four lines work out arithmetically by placing the 16 digits listed below into the 16 gaps.  Can you  achieve it?

0    0    1    1    2    2    3    3    4    4    5    6    6    7    8    9

◯  +  ◯   =    8    =   ◯  +  ◯
◯  +  ◯   =    7    =   ◯  –  ◯
◯  +  ◯   =    6    =   ◯  ×  ◯
◯  +  ◯   =    4    =   ◯  ÷  ◯

Full details can be found at Mathelona. The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 2nd & 5th rows of the playing board contain the following fourteen numbers:

6   7   8   16   17   21   28   48   50   55   63   64   81   84

How many factors does the smallest number in the list have? 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 SIXTEEN different ways to make 210 when using Lagrange’s Theorem. How many can you find? The Mathematically Possible Challenge

Using 57 and 11 once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

1    3    5    7    9    11    13    15    17    19

#OddNumbers The Target Challenge

Can you arrive at 210 by inserting 5, 10, 12 and 18 into the gaps on each line?

•  ◯×◯+◯×◯ = 210
•  (◯–◯÷◯)×◯ = 210   