# day/dydd 26 at 7puzzleblog.com The Main Challenge

From the numbers 50-100 inclusive, eliminate all multiples of 5, prime numbers, even numbers and multiples of 3. What is the sum of the two numbers that remain? 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 difference between the two multiples of 10? 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 26 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

70    71    72    73    74    75    76    77    78    79

#NumbersIn70s

The Target Challenge

Can you arrive at 26 by inserting 2, 4, 5 and 8 into the gaps on both lines?

•  ◯²+(◯×◯÷◯) = 26
•  (◯+◯)×◯÷◯ = 26
•  (◯+◯)×◯+◯ = 26   