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T he Main Challenge

Read the following facts:

  •  I am a 2-digit number,
  •  both my digits are odd,
  •  the sum of both digits is less than 10,
  •  my 1st digit is smaller than my 2nd digit, and
  •  I am a multiple of 3.

Which number am I?

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 3rd & 4th rows of the playing board contain the following fourteen numbers:

3   10   13   25   32   35   36   42   44   45   54   60   66   80

From the list, what is the sum of the multiples of 10?

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 NINE different ways to make 219 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Using 46 and once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

12    24    36    48    60    72    84    96    108    120


The Target Challenge

Can you arrive at 219 by inserting 349 and 16 into the gaps on each line?

  •  (◯×◯+◯)×◯ = 219
  •  ◯²×◯–(◯+double◯) = 219

Answers can be found here.

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