# DAY/DYDD 27: The Main Challenge

Using each of the numbers 2, 2 and 5 exactly once each, with + – × ÷ available, can you find all NINE numbers from 1-20 that are mathematically possible to make? 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

How many more even numbers than odd numbers are listed? 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 27 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 TWO numbers it is possible to make from the list below?

3    6    9    12    15    18    21    24    27    30

#3TimesTable

The Target Challenge

Can you arrive at 27 by inserting 3, 3, 4 and 6 into the gaps on each line?

•  (◯+◯)×◯+◯ = 27
•  ◯²+◯◯×◯ = 27
•  ◯×◯+√(◯×◯) = 27
•  (◯+◯)×◯◯ = 27
•  (◯²+◯²)×◯÷◯ = 27 Answers can be found here. Click Paul Godding for details of online maths tuition. This entry was posted in 7puzzleblog.com. Bookmark the permalink.

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