DAY/DYDD 97:

The Main Challenge

When each letter of the English alphabet is given a numerical value, A=1 B=2 C=3 . . . Z=26, and the values of the individual letters are added together, which day of the week has the highest total and which has the lowest total?

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

What is the sum of the four biggest numbers?

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 97 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 57 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

#10TimesTable

The Target Challenge

Can you arrive at 97 by inserting 2, 3, 5 and 10 into the gaps on each line?

  •  ◯××◯– = 97
  •  ◯³×²+(◯–◯)² = 97
  •  ²×◯+◯+◯ = 97

Answers can be found here.

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