DAY 164:

The Main Challenge

You have 12 balls and each ball is numbered differently from 1 to 12.  They are randomly placed into two bags so each bag contains the six numbered balls shown below:

  • Red bag:   2, 3, 4, 6, 9, 11
  • Blue bag:  1, 5, 7, 8, 10, 12

You then move a ball from the red bag to the blue bag.  The total of the seven balls in the blue bag is now double the total of the five balls left in the red bag.

Which ball did you move from the red bag to the blue bag?

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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

How many pairs of numbers have a difference of 12?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 164, in SIX different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using the three digits 35 and 8 once each, with + – × ÷ available, which are the only FOUR numbers it’s possible to make from the list below?

2    3    5    7    11    13    17    19    23    29

#PrimeNumbers

The Target Challenge

Can you arrive at 164 by inserting 467 and 8 into the gaps on each line?

  •  (◯×◯–◯)× = 164
  •  ◯²×◯–quarter(³)– = 164

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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