# DAY/DYDD/PÄIVÄ/NAP 41 T he Main Challenge

When a certain 4-digit number is multiplied by 4, its digits appear in reverse order. It also has both of these properties:

•  its first digit is a quarter of the last one, and
•  its second digit is one less than the first.

What number must it be? The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 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

List four pairs of numbers that have a difference of 7. 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 THREE ways of making 41 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 26 and 11 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

1     8     25     64     125

#CubeNumbers

The Target Challenge

Can you arrive at 41 by inserting 3, 5, 7 and 9 into the gaps on each line?

•  ◯×◯+◯–◯ = 41
•  (◯+◯)×◯–◯ = 41
•  (◯–◯)×◯+ = 41   