# DAY/DYDD/PÄIVÄ/NAP 16

The Main Challenge

What is the sum of the 50 integers (or whole numbers) from 1 through to 50 inclusive?

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 1st & 7th rows contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

What is the sum of the factors of 24 listed above?

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 only TWO ways of making 16 when using Lagrange’s Theorem. Can you find both?

The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

6    12    18    24    30    36    42    48    54    60

#6TimesTable

The Target Challenge

Can you arrive at 16 by inserting 3, 4, 6 and 8 into the gaps on each line?

•  ◯×◯×◯÷◯ = 16
•  ◯²–◯×(◯–◯) = 16
•  ÷◯×³√◯×◯ = 16