# day/dydd 79 at 7puzzleblog.com

T he Main Challenge

If each letter is assigned a value as follows, A=1 B=2 C=3 … Z=26, can you find a 7-letter word in the English language that has the value of 79 when the values of all seven letters are added together?

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 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

How many factors of 60 are listed above?

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 THREE ways of making 79 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 23 and 11 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

4    8    12    16    20    24    28    32    36    40

#4TimesTable

The Target Challenge

Can you arrive at 79 by inserting 2, 5, 9 and 10 into the gaps on each line?

•  (◯+◯)×◯+ = 79
•  (◯+◯)×◯–◯⁴ = 79
•  ◯²+◯×(◯–◯²) = 79