No if() Only abs()
Good point. Nod. But we have to exclude 0. Whatever, the question should just emphasize on "pure arithmetic" or ask for an algebra expression. context 
9
5
Sum of Two Prime Numbers
If p, q > 2 are consecutive in set of primes. Since p,q can only be odd number, (p+q) is an even number.
Can (p+q)/2 be prime?
from http://republicofmath.com/

Doable

2
2
How far can you go?
You have a 4 wheels car and a spare tire in the trunk.
The tire being used will be worn off for 1/4 part of it per mile (completely wear out for 4 miles)
How to make use of the spare tire to go as fa
...

Hard

2
2
Cut the pizza into 11 equal slices with a wrist watch
Tools:
(1) A wrist watch and (2) a normal knife
Goal:
Slice a pizza into 11 equal pieces

Hard

30
19
No if() Only abs()
Given two variable a and b, construct a function f(a,b) which return the maximum one in {a,b}.
You can only use + · / and abs() (to take the absolute value). NO if() is allowed in your construction.
...

Doable
