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T he Main Challenge

Today’s task is to multiply two numbers together, then either add or subtract the third number to achieve the target answer of 37.

Using the formula (a×b)±c, where a, b and c are three unique digits from 1-9, one way of achieving 37 is (7×5)+2; can you find the other SEVEN ways?

[Note: (7×5)+2 = 37 and  (5×7)+2 = 37 counts as just ONE way.]

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 5th & 6th rows of the playing board contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

From the list, which three different numbers have a sum of 100?

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 is only ONE way to make 224 when using Lagrange’s Theorem. Can you find it?

The Mathematically Possible Challenge

Using 46 and once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

13    26    39    52    65    78    91    104    117    130


The Target Challenge

Can you arrive at 224 by inserting 127 and 7 into the gaps on each line?

  •  ◯×◯²×(◯+◯) = 224
  •  ◯⁵×◯³×◯²÷◯ = 224

Answers can be found here.

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