DAY/DYDD 36:

The Main Challenge

You’ve rolled the numbers 2, 3 and 4 with your three dice.  Using these once each, with + – × ÷ available, what is the lowest positive whole number it is NOT possible to make?

Visit Roll3Dice.com for further details of similar challenges.

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 & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

Which three different numbers 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 FOUR ways of making 36 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 26 and 11 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

1    4    9    16    25    36    49    64    81    100

#SquareNumbers

The Target Challenge

Can you arrive at 36 by inserting 2, 3, 4 and 6 into the gaps on each line?

  •  (◯+◯+◯)× = 36
  •  (◯²+◯)×◯÷ = 36
  •  (◯–◯)×◯× = 36
  •  ◯²×(◯+◯–◯) = 36  (2 different ways)

Answers can be found here.

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