DAY/DYDD 90:

The Main Challenge

When playing the brilliant 24game, your task is to arrive at the target answer of 24.

Each of the four numbers 0.5, 1, 5 and 10 must be used exactly once each in your calculation.  The four operations, + – × and ÷, are available to use.  Can you make 24?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 4th & 5th rows contain the following fourteen numbers:

3   6   7   10   16   21   32   35   44   50   54   60   81   84

What is the product of the highest and lowest numbers on the list?

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 NINE ways of making 90 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 57 and 10 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

3    6    9    12    15    18    21    24    27    30

#3TimesTable

The Target Challenge

Can you arrive at 90 by inserting 3, 6, 8 and 9 into the gaps on each line?

  •  ◯×+◯× = 90
  •  (◯+◯)×◯–◯ = 90
  •  (◯+◯÷◯)×◯ = 90

Answers can be found here.

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