# day/dydd 14 at 7puzzleblog.com The Main Challenge

Insert the 12 numbers 1 1 2 2 2 3 5 5 6 7 8 and 8 so that all three lines work out arithmetically:

◯  +  ◯   =     6     =   ◯  –  ◯
◯  +  ◯   =    14    =   ◯  ×  ◯
◯  +  ◯    =    5     =   ◯  ÷  ◯

If you enjoyed trying this puzzle, visit our Mathelona page for further details. 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 5th & 6th rows contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

What is the difference between the highest and lowest odd numbers? 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 is only ONE way of making 14 when using Lagrange’s Theorem. Can you find it? The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which is the ONLY number 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 14 by inserting 2, 4, 5 and 5 into the gaps on each line?

•  ◯+◯+◯+√◯ = 14
•  ◯²–(◯+◯+◯) = 14
•  (◯+÷◯)× = 14   