DAY/DYDD 84:

T he Main Challenge

Follow these six steps:

  1.  Work out the sum of 3 and 5,
  2.  Calculate the difference between 3 and 5,
  3.  Find the product of the two answers in Points 1 and 2,
  4.  Find the square root to your answer in Point 3,
  5.  Add the answer in Point 4 to your answer in Point 1,
  6.  Subtract your answer in Point 2 from the answer in Point 5.

What is your answer after carrying out Point 6?

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 2nd & 3rd rows contain the following fourteen numbers:

8   13   17   25   28   36   42   45   48   55   63   64   66   80

Which pair of numbers have a difference of 49?

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

The Mathematically Possible Challenge

Using 23 and 11 once each, with + – × ÷ available, which is the ONLY number that is possible to make from the list below?

9    18    27    36    45    54    63    72    81    90

#9TimesTable

The Target Challenge

Can you arrive at 84 by inserting 2, 3, 6 and 7 into the gaps on each line?

  •  (◯+◯)²+◯–◯² = 84
  •  (◯×◯+◯)× = 84
  •  ((◯–◯)²–◯)×◯ = 84

Answers can be found here.

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