DAY/DYDD 18:

The Main Challenge

All nine numbers from 21 to 29 inclusive must be allocated to a letter below so that each allocated number satisfies the condition given on the line:

  •  (a)  even number,
  •  (b)  factor of 144,
  •  (c)  power of 3,
  •  (d)  prime number,
  •  (e)  digits which differ by 1,
  •  (f)  exactly 3 factors,
  •  (g)  multiple of 7,
  •  (h)  equal to the sum of all its factors (except the number itself),
  •  (i)   2nd digit is greater than its 1st digit.

Remember, the numbers 21 to 29 should only appear once each.

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 1st & 7th rows contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

Which odd number, when 21 is added 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 THREE ways of making 18 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which are the only TWO numbers it 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 18 by inserting 2, 3, 4 and 6 into the gaps on each line?

  •  ◯×◯–◯×◯ = 18
  •  ◯÷◯×◯×◯² = 18
  •  (◯÷◯)³×√◯÷◯ = 18

Answers can be found here.

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