# DAY/DYDD 134: The Main Challenge

Read the following facts to work out my numerical value:

•  I am a single digit number,
•  If you add 6 to me I become a 2-digit number,
•  I am an odd number,
•  I am not a square number,
•  I am a factor of 30. 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 & 6th rows contain the following fourteen numbers:

5   12   13   18   20   25   33   36   42   45   49   56   66   80

What is the difference between the highest prime number and the highest odd 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 SEVEN ways of making 134 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 36 and 10 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 134 by inserting 2, 3, 5 and 6 into the gaps on each line?

•  ◯³+◯×◯÷◯ = 134
•  (◯+◯)²+◯²+◯² = 134   