# day/dydd 59 at 7puzzleblog.com

T he Main Challenge

Your starting number is 18 and your task is to arrive at the same final answer.  There are ten arithmetical steps from beginning to end, each one involving a whole number, but the 9th (and penultimate) step is missing!  What must it be?

÷2   +3   –8   ×6   +4   –3   ÷5   ×2   ?   ×2   =   18

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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

What is the difference between the lowest and highest multiples of 4?

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 59 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which FOUR numbers is it 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 59 by inserting 4, 5, 6 and 10 into the gaps on each line?

•  ◯×+ = 59
•  ◯²+◯×◯+ = 59
•  (◯+◯)×◯– = 59

Answers can be found here.

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