DAY/DYDD 59:

The 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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