DAY/DYDD 119:

The Main Challenge

Using the numbers 3, 6 and 6 just once each, and with + – × ÷ available, which THREE of the following target numbers are NOT mathematically possible to achieve?

1    2    3    4    6    8    9    12    15    18    21    24

This is from our innovative board game, Mathematically Possible, details of which can be found by visiting the game’s own website.

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 contain the following fourteen numbers:

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

Which number, when adding 50 to it, becomes a square number?

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 FOUR ways of making 119 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 24 and 12 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

7    14    21    28    35    42    49    56    63    70

#7TimesTable

The Target Challenge

Can you arrive at 119 by inserting 2, 6, 9 and 11 into the gaps on each line?

  •  (◯+◯)×(◯–◯) = 119
  •  ◯×◯×◯+◯ = 119

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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