DAY/DYDD 52:

The Main Challenge

List the FIVE 2-digit numbers to have the following attributes:

  •  are not odd numbers,
  •  are not multiples of 3, 4, or 7,
  •  has its digits adding up to more than 10.

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 1st & 5th rows contain the following fourteen numbers:

2   6   7   9   14   15   16   21   22   40   50   72   81   84

What is the sum of the factors of 36 listed above?

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 FIVE ways of making 52 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 89 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

60    61    62    63    64    65    66    67    68    69

#NumbersIn60s

The Target Challenge

Can you arrive at 52 by inserting 4, 6, 8 and 9 into the gaps on each line?

  •  ◯×◯–◯÷◯ = 52
  •  ◯²–(◯+√◯×√◯) = 52
  •  ◯²+◯×(◯–◯)² = 52
  •  (√◯×◯+◯)×√ = 52

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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2 Responses to DAY/DYDD 52:

  1. Hitesh says:

    Very interesting puzzles Paul…I had to check the answers…

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