There are three type of amount currencies that is less than 10 namely: 1, 2, and 5
. You are going to drug store, supermarket, restaurant today where you will have three exchanges(buy medicine, buy goods, eat food ). For convenience you don't want to any changes which are less than 10 denomination(amount type of 1, 2, and 5) in these three exchanges, How many changes with amount type of 1, 2, 5 should you bring respectively at least?
My thought is: if there is only one exchange involved, you'd bring number of small changes 1, 2, and 5 whose sum combination equal any integer numbers from 1 to 9. So I get the result list{1, 2, 2, 5}
i.e. one number of one amount currency, two number of two amount currency, and one number of five amount currency. Now considering three exchanges, I'd simply multiply this with three so the result list is {1, 1, 1, 2, 2, 2, 2, 2, 2, 5, 5, 5}
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Is my reasoning correct? and How will you think this question?