# day/dydd 219 at 7puzzleblog.com T he Main Challenge

•  I am a 2-digit number,
•  both my digits are odd,
•  the sum of both digits is less than 10,
•  my 1st digit is smaller than my 2nd digit, and
•  I am a multiple of 3.

Which number am I? 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

From the list, what is the sum of the multiples of 10? 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 NINE different ways to make 219 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?

12    24    36    48    60    72    84    96    108    120

#12TimesTable The Target Challenge

Can you arrive at 219 by inserting 349 and 16 into the gaps on each line?

•  (◯×◯+◯)×◯ = 219
•  ◯²×◯–(◯+double◯) = 219   