DAY/DYDD 126:

The Main Challenge

You have SIX each of 7puzzleland‘s brand-new 4p and 7p coins. Your task is to try and make various amounts from 20p and above with these coins.

As shown here, the first few have been done for you:

  • 20p can be made from 5 × 4p coins,
  • 21p from 3 × 7p coins,
  • 22p from 2 × 7p coins and 2 × 4p coins . . .

From 20p upwards, what is the lowest amount you CANNOT make from your 12 coins?

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 2nd & 4th rows contain the following fourteen numbers:

3   8   10   17   28   32   35   44   48   54   55   60   63   64

What is the difference between the highest multiple of 11 and lowest multiple of 7?

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 EIGHT ways of making 126 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 24 and 12 once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

40    41    42    43    44    45    46    47    48    49

#NumbersIn40s

The Target Challenge

Can you arrive at 126 by inserting 2, 3, 6 and 9 into the gaps on each line?

  •  ◯×◯×(◯–◯) = 126
  •  ◯×(◯×◯–◯²) = 126
  •  ◯²×◯+◯×◯ = 126
  •  ◯³×◯–◯²×◯ = 126
  •  ◯²×◯+double(◯×◯) = 126

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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