Hit each target using only one repeated digit and arithmetic, and the fewer copies of that digit you use, the higher you score.
Every puzzle gives you a single digit. Build expressions that reach each target using only that digit plus the operators plus, minus, times, divide, power and parentheses (you can concatenate, like writing 55). Some tiers want an exact value; others want the right remainder modulo a number. Use fewer copies of the digit to score more.
Sieve is in the spirit of single-digit arithmetic puzzles, rewarding clean logical reasoning.
Reaching every target using a single repeated digit and a handful of operators is the four fours puzzle, generalised. Its first printed appearance was in Knowledge: An Illustrated Magazine of Science in 1881.
Allowing concatenation — writing 55 from two fives — and asking some tiers for a remainder rather than an exact value are the original extensions.
The remainder tiers change the search completely. Hitting a value exactly is a matter of expression-building; hitting the right residue is modular arithmetic, where enormous expressions and tiny ones can be equally correct.
Sieve is an original free browser math game in the spirit of single-digit arithmetic puzzles, rewarding clever, economical expressions and a feel for number structure and modular arithmetic.