DAY/DYDD 19:

The Main Challenge

Only one of the following 3-digit numbers is divisible by 3. Which one?

136   139   245   248   353   357   466   469   572   578   680

[Note: If you don’t know the trick on how to work this out, please get in touch.]

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 1st & 7th rows contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

What is the sum of the multiples 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 TWO ways of making 19 when using Lagrange’s Theorem. Can you find both?

The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which are the only TWO numbers it is 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 19 by inserting 1, 2, 3 and 4 into the gaps on each line?

  •  (◯+◯)×+◯ = 19
  •  (◯+◯)×◯–◯ = 19
  •  ◯²+(◯+◯ = 19

Answers can be found here.

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