DAY/DYDD 135:

The Main Challenge

Here’s a number trail involving 16 arithmetical steps.  Start with the number 2, then:

  •  +33
  •  divide by seven
  •  ×3
  •  add ten percent
  •  double this
  •  add three
  •  find the square root of this
  •  +7
  •  1/2 of this
  •  add nineteen point five
  •  subtract two
  •  ÷6
  •  +15
  •  ×5
  •  –93
  •  ÷2

What is your final answer?

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 3rd & 6th rows contain the following fourteen numbers:

5   12   13   18   20   25   33   36   42   45   49   56   66   80

Which two numbers, when doubled, are also present 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 SEVEN ways of making 135 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

10    20    30    40    50    60    70    80    90    100

#10TimesTable

The Target Challenge

Can you arrive at 135 by inserting 4, 5, 9 and 12 into the gaps on each line?

  •  ◯²–◯×(◯–◯) = 135
  •  ◯×◯×◯÷◯ = 135
  •  (◯+◯)²+half(◯×◯) = 135

Answers can be found here.

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