DAY/DYDD 48:

The Main Challenge

What is the biggest integer (whole number) less than 630,000 that can be written using all six digits from 1 to 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 3rd & 7th rows contain the following fourteen numbers:

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

From the list, find three different numbers that 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 are TWO ways of making 48 when using Lagrange’s Theorem. Can you find both?

The Mathematically Possible Challenge

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

9    18    27    36    45    54    63    72    81    90

#9TimesTables

The Target Challenge

Can you arrive at 48 by inserting 4, 4, 5 and 8 into the gaps on each line?

  •  ◯×◯+◯+ = 48
  •  ◯×◯×(◯–◯) = 48
  •  ◯²+–(◯×◯) = 48

Answers can be found here.

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