# day/dydd 93 at 7puzzleblog.com T he Main Challenge

Your task is to arrive at the target answer of 18 by using each of the four numbers 2, 6, 7 and 10 exactly once each, with + – × ÷ available. Can you find TWO ways of making 18? The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 6th & 7th rows contain the following fourteen numbers:

4   5   11   12   18   20   24   27   30   33   49   56   70   77

Which number, when 23 is added to it, becomes a square number? 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 FIVE ways of making 93 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 57 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

6    12    18    24    30    36    42    48    54    60

#6TimesTable

The Target Challenge

Can you arrive at 93 by inserting 3, 4, 6 and 11 into the gaps on each line?

•  (◯+◯)×◯+◯ = 93
•  ◯²–◯²–◯²–half = 93
•  ◯³+◯×◯+◯ = 93   