The cells of a 3 x 3 grid contain prime digits. When read by columns, rows and diagonals,
as well as in the reverse directions, they form 3-digit prime numbers, and the total of their respective digits is also prime ("magenta" and "salmon" coloured cells).
Find 3 different grid arrangements which are not mere transformations of each other (like mirrors or rotations). Note that some mirrors or rotations might not even work in this scheme, while others would.
Note:
1. There are at least two other arrangements where a non-prime digit may be used, and digit totals are not always prime.
2. This is a relatively easy exercise with just a calculator.
Through a marksmanship contest, there are 4 strings of 4 glass balls hanging down from a horizontal post. Each bullet can only hit one glass ball at a time, so 16 shots need to be fired.
The only problem is if you shoot a glass ball that has a glass ball hanging below it (on the same string), it will fall off. So given the rule that you can't shoot a glass ball with a glass ball underneath it (and on the same string), how many ways can you shoot all the glass balls?
Latest: 
Bonus: 
