# day/dydd 111 at 7puzzleblog.com T he Main Challenge

This describes a particular number less than 100:

•  its digits add up to 12,
•  if the unit digit is subtracted from the tens digit, then doubled, the answer is also 12.

What is the number? 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 contain the following fourteen numbers:

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

List THREE different numbers that have a sum of 77. 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 FIVE ways of making 111 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 14 and once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

9    18    27    36    45    54    63    72    81    90

#9TimesTable

The Target Challenge

Can you arrive at 111 by inserting 2, 3, 5 and 7 into the gaps on both lines?

•  (◯×◯+◯)×◯ = 111
•  (◯+◯)²+double(◯×◯) = 111   