Henry I. answered 09/24/15
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As you have no doubt figured out, this is a logic problem, not really a "math" problem, if we can differentiate.
Notice that the list of zingers 5, 41, etc., all have digits that add up to 5. We can confirm the pattern by observing that the list of non-zingers 7, 22, etc., contains NO groups that add up to 5. Therefore, the definition of a zinger is any integer whose digits have a cum of 5.
Examine the final list for that quality to determine which are and which are not zingers.