DAY 170:

The Main Challenge

Study the seven clues and place the numbers 1-9 into the nine positions on this 3-by-3 grid. Each number should appear exactly once:

x              x              x

x              x              x

x              x              x

Clues:

  1.  The 8 is directly above the 5,
  2.  The 6 is further right than the 7,
  3.  The 7 is further right than the 1,
  4.  The 1 is lower than the 5,
  5.  The 5 is further right than the 9,
  6.  The 3 is higher than the 9 and further right than the 2,
  7.  The 4 is higher than the 7 and further right than the 8.

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 2nd & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

What is the difference between the sum of the highest and lowest even numbers and the product of the highest and lowest even numbers?

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 170, in TEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which is the ONLY target number it’s possible to make from the list below?

9    18    27    36    45    54    63    72    81    90

#9TimesTable

The Target Challenge

Can you arrive at 170 by inserting 9, 10, 20 and 20 into the gaps on each line?

  •  ◯+◯×◯–◯ = 170
  •  (◯–◯÷◯)×◯ = 170

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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