# day/dydd 230 at 7puzzleblog.com T he Main Challenge

Use all three numbers in each of the five groups below, with + – × ÷ available, to try and make the target of 23. But for one of the groups it is impossible, which one?

•   1    4    6
•   2    5    5
•   3    4    5
•   3    4    6
•   3    5    6

Full details of our number & strategy board game, click Mathematically Possible. 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 1st & 7th rows of the playing board contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

Which three different numbers have a sum of 77? 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 THIRTEEN different ways to make 230 when using Lagrange’s Theorem. How many can you find? The Mathematically Possible Challenge

Using 24 and once each, with + – × ÷ available, which is the ONLY number is it possible to make from the list below?

7    14    21    28    35    42    49    56    63    70

#7TimesTable The Target Challenge

Can you arrive at 230 by inserting 2, 3, 5, 6 and 7 into the gaps below?

•  ◯×(◯+◯)²+◯×◯ = 230   