There are five products in a store; let's call them A, B, C, D, and E.
The prices of those products are all integers between one and five cents each.
When you pay, the sum is rounded to the closest five cents.
Let's assume that your account is fined with half a point every time your purchase is not an integer multiplication of five cents.
The price of A is one cent, but you don't know anything about the prices of B-E, nor are you aware of the fines you accumulate along the way. The only information you get, at the end of the month, is whether the cumulative number of points you were fined is an integer or not.
For example, after buying the following six purchases: AB AC AABC AAABCC AAABBC BBBBC you can know whether B and C are both 4 or not.
Can you devise a set of purchases, one for each day, such that at the end of the month you'd be able to know whether or not the prices of B-E have exactly two different values?
Please submit your answer as at most 31 lines (one per day) where each line contains a list of items you buy on that day.
We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!
We invite visitors to our website to submit an elegant solution. Send your submission to the webmaster.
If you have any problems you think we might enjoy, please send them in. All replies should be sent to: webmster@us.ibm.com
Consider Sequence A185028 of the Online Encyclopedia of Integer Sequences.Can you answer the question that appears in the "COMMENTS"? Specifically, can you prove or disprove the finiteness of the sequence? The sequence and the question were both formulated by Moshe Wolf. It got to me in riddle form by Oded Margalit. Thanks, Oded and Moshe!
