# day/dydd 28 at 7puzzleblog.com The Main Challenge

Here is an introductory Mathelona challenge taken from the front cover of Volume 1 of my pocket book series.

◯  +  ◯   =    3    =   ◯  –  ◯
◯  +  ◯   =    4    =   ◯  ×  ◯
◯  +  ◯   =    5    =   ◯  ÷  ◯

Can you insert the digits 1 1 1 1 2 2 2 3 3 4 5 and 6 into the 12 gaps above so all three lines work out arithmetically? The 7puzzle Challenge

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

The 3rd & 6th rows contain the following fourteen numbers:

5   12   13   18   20   25   33   36   42   45   49   56   66   80

What is the sum of the odd numbers listed above? 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 THREE ways of making 28 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 26 and 11 once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

4    8    12    16    20    24    28    32    36    40

#4TimesTable

The Target Challenge

Can you arrive at 28 by inserting 2, 4, 6 and 8 into the gaps on each line?

•  ◯×◯+◯–◯ = 28
•  ◯×◯÷◯+◯ = 28
•  ◯×◯+◯×√◯ = 28
•  ◯×◯+◯÷◯ = 28
•  (◯+◯)×◯–◯ = 28
•  (◯+◯)×◯÷◯ = 28
•  (◯+◯)×+◯ = 28   