Place eggs in single layer in saucepan; add enough water to completely cover eggs by at least 1 inch. Bring water to boil; cover. Remove saucepan from heat; let stand 15 minutes. Drain eggs; immediately place in bowl of ice water. Let stand until completely cooled, changing water if necessary. Perfectly hard-cooked eggs will have a firm yellow center with no greenish tinge. Hard-cooked eggs in their shells can be refrigerated for up to one week.