# day/dydd 178 at 7puzzleblog.com T he Main Challenge

Can you arrive at the target answer of 7 by using each of the numbers 0.2, 0.5, 2 and 2.5 exactly once each, and with +  × ÷ available? The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

What is the sum of the factors of 36? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 178, in TWELVE different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 36 and 12 once each, with + – × ÷ available, which SEVEN target numbers from the list below can be made?

6    12    18    24    30    36    42    48    54    60

#6TimesTable The Target Challenge

Can you arrive at 178 by inserting 10, 11, 16 and 20 into the gaps on each line?

•  ◯×◯+◯÷◯ = 178
•  ◯×◯+double(◯–◯) = 178   