# DAY/DYDD/PÄIVÄ/NAP 44

T he Main Challenge

If the number sequence 2, 5, 8, 11, 14 . . . is continued, which is the ONLY number from the following list that will appear later in the sequence?

22   34   43   57   65   72   85   99

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 & 6th rows contain the following fourteen numbers:

5   8   12   17   18   20   28   33   48   49   55   56   63   64

What is the difference between the sum of the odd numbers and the sum of the even 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 TWO ways of making 44 when using Lagrange’s Theorem. Can you find both?

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?

5    10    15    20    25    30    35    40    45    50

#5TimesTable

The Target Challenge

Can you arrive at 44 by inserting 2, 4, 6 and 7 into the gaps on each line?

•  (◯+◯)×(◯–◯) = 44
•  ◯²–(◯+◯)÷ = 44
•  (◯×◯–◯)×◯ = 44
•  ◯²+(◯–◯)×◯ = 44