DAY/DYDD 99:

The Main Challenge

Read the following ten clues about a particular number:

  • it’s less than 100,
  • it’s one more than a multiple of 3,
  • exactly one of its two digits is prime,
  • you get a prime if you reverse its digits,
  • it’s not a multiple of 5,
  • it’s not a prime number,
  • it has exactly four factors,
  • it’s not a square number,
  • the sum of its digits is prime,
  • if you multiply it by 5, the answer is greater than 100.

Can you find the mystery number?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 1st & 3rd rows contain the following fourteen numbers:

2   9   13   14   15   22   25   36   40   42   45   66   72   80

How many multiples of 12 are 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 SIX ways of making 99 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 57 and 10 once each, with + – × ÷ available, which TWO numbers it is possible to make from the list below?

12    24    36    48    60    72    84    96    108    120

#12TimesTable

The Target Challenge

Can you arrive at 99 by inserting 2, 3, 5 and 9 into the gaps on each line?

  •  (×◯+)×◯ = 99
  •  ◯×◯×◯+² = 99
  •  (+)²+² = 99
  •  ◯²×◯²–²÷◯ = 99

Answers can be found here.

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