DAY/DYDD 49:

T he Main Challenge

You roll two normal six-sided dice, both containing the numbers 1-6.  When multiplying the two numbers that show, how many DIFFERENT answers is it possible to obtain?

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 3rd & 7th rows contain the following fourteen numbers:

4   11   13   24   25   27   30   36   42   45   66   70   77   80

What is the sum of the factors of 90?

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 FOUR ways of making 49 when using Lagrange’s Theorem. Can you find them?

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?

10    20    30    40    50    60    70    80    90    100

#10TimesTables

The Target Challenge

Can you arrive at 49 by inserting 1, 2, 3 and 4 into the gaps on each line?

  •  (+)²×()² = 49
  •  (+)²×√◯ = 49
  •  ◯(+)×◯ = 49

Answers can be found here.

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