# DAY/DYDD/PÄIVÄ/NAP 85 T he Main Challenge

Find the sum of the following three numbers:

• twelve thousand and two
• thirty five thousand and thirty-five
• fifty five thousand, one hundred and fifty-five 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 9 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 FIVE ways of making 85 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?

10    20    30    40    50    60    70    80    90    100

#10TimesTable

The Target Challenge

Can you arrive at 85 by inserting 5, 10, 15 and 20 into the gaps on each line?

•  ◯×◯+◯– = 85
•  ◯²+◯×(◯÷◯)² = 85
•  (◯+÷)×◯ = 85   