# day/dydd 195 at 7puzzleblog.com T he Main Challenge

In this Kakuro-style question, can you list the ONLY way possible to make 16 when adding together five unique digits from 1-9? The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 4th & 5th rows of the playing board contain the following fourteen numbers:

3   6   7   10   16   21   32   35   44   50   54   60   81   84

How many pairs of numbers differ by exactly 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).

Show how you can make 195, in TEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

1     8     27     64     125

#CubeNumbers The Target Challenge

Can you arrive at 195 by inserting 5, 8, 13 and 18 into the gaps on each line?

•  (◯+◯+◯)×◯ = 195
•  (◯+◯–◯)×◯ = 195   