# day/dydd 117 at 7puzzleblog.com Th e Main Challenge

Can you place the 12 numbers 1 1 2 2 3 3 4 5 6 7 8 and 10 into the 12 gaps below so all four lines work out arithmetically?

◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯

If you enjoy this type of number puzzle, click on this Mathelona link. 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

Which four different numbers have a sum of 100? 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 EIGHT ways of making 117 when using Lagrange’s Theorem. Can you find them all? The Mathematically Possible Challenge

Using 24 and 12 once each, with + – × ÷ available, which FIVE 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 117 by inserting 3, 6, 9 and 12 into the gaps on each line?

•  ◯×◯+◯+◯ = 117
•  ◯²+◯×(◯–◯) = 117   (2 different ways!)   