# DAY/DYDD 218: T he Main Challenge

From all the odd numbers in the range 1-23 inclusive, eliminate all prime numbers and multiples of 3. Which is the only number that remains? 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 3rd & 4th rows of the playing board contain the following fourteen numbers:

3   10   13   25   32   35   36   42   44   45   54   60   66   80

Which number, when 10 is added to it, becomes a square number? 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 ELEVEN different ways to make 218 when using Lagrange’s Theorem. How many can you find? The Mathematically Possible Challenge

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

11    22    33    44    55    66    77    88    99    110

#11TimesTable The Target Challenge

Can you arrive at 218 by inserting 41012 and 17 into the gaps on each line?

•  ◯×◯+◯+◯ = 218
•  ◯×◯+◯×◯ = 218
•  ◯²–◯×(◯–◯)+1 = 218
•  ◯×(◯+◯)+treble◯–1 = 218   