DAY/DYDD 46:

The Main Challenge

The smallest positive integer that has exactly three factors is FOUR; these are 1, 2 and 4. Find the next integer to have just three factors and the product of these three numbers.

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 3rd & 7th rows contain the following fourteen numbers:

4   11   13   24   25   27   30   36   42   45   66   70   77   80

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 TWO ways of making 46 when using Lagrange’s Theorem. Can you find both?

The Mathematically Possible Challenge

Using 89 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

7    14    21    28    35    42    49    56    63    70

#7TimesTables

The Target Challenge

Can you arrive at 46 by inserting 3, 4, 5 and 9 into the gaps on each line?

  •  (◯+◯)×◯+ = 46
  •  ◯²+◯×◯+ = 46
  •  ◯×◯+◯–√◯ = 46

Answers can be found here.

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