DAY/DYDD/PÄIVÄ/NAP 83

T he Main Challenge

What is the sum of the multiples of 0.5 in the range 10 to 20 inclusive?

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 2nd & 3rd rows contain the following fourteen numbers:

8   13   17   25   28   36   42   45   48   55   63   64   66   80

How many multiples of 3 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 FOUR ways of making 83 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 23 and 11 once each, with + – × ÷ available, which is the ONLY number that is possible to make from the list below?

8    16    24    32    40    48    56    64    72    80

#8TimesTable

The Target Challenge

Can you arrive at 83 by inserting 2, 5, 8 and 9 into the gaps on each line?

•  (◯+◯)×◯– = 83  (2 different ways)
•  ◯²+◯×◯+ = 83
•  ((◯+◯)²–√◯)÷◯ = 83