# DAY/DYDD/PÄIVÄ/NAP 66

T he Main Challenge

When multiplying two numbers together and then adding or subtracting a third number, there are four ways of reaching 60 when the three numbers used in each calculation are in the range 1-9, and can be repeated.

One way to make 60 is (9×6)+6; can you find the other three?

[Note:  (9×6)+6 and (6×9)+6 counts as just one way.]

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 & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

How many pairs of consecutive numbers are there?

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

The Mathematically Possible Challenge

Using 46 and 12 once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?

3    6    9    12    15    18    21    24    27    30

#3TimesTable

The Target Challenge

Can you arrive at 66 by inserting 2, 3, 4 and 9 into the gaps on each line?

•  (◯×◯+◯)× = 66
•  (◯×◯–◯)× = 66
•  ◯²×◯+◯× = 66
•  ◯³+(◯+◯)²+√◯ = 66