# DAY/DYDD 173: T he Main Challenge

When allocating each letter of the English alphabet a numerical value as follows; A=1 B=2 C=3 … Z=26, the value of the word SUM, for example, would be 19+21+13 = 53.

What would be the value of our popular number puzzle, MATHELONA? The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

Find three pairs of numbers that have a sum that is also on the list. The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 173, in SEVEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which THREE target numbers is it possible to make from the list below?

1     8     27     64     125

#CubeNumbers The Target Challenge

Can you arrive at 173 by inserting 5, 7, 14 and 15 into the gaps on each line?

•  (◯×◯)+(◯×◯) = 173
•  ◯×(◯+◯)–half◯ = 173   