# Each true hour at least two of my clocks chime. Prove we can throw away three of the five clocks and still hear a chime at each true hour.

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### 1 Answer

At least 2 clocks chiming at true time implies one of the following exclusive 4 possibilities:

(i) Only particular 2 clocks are chiming at the true time or

(ii) only particular 3 clocks are chiming at the true time or

(iii) only particular 4 clocks are chiming at the true time or

(iv) only particular 5 clocks are chiming at the true time.

At the true time with chiming, you can identify which is not chiming at true time. Identify which are not chiming clocks and separate them. If it is the first case it is 3 to separate. If it is the second case, you identify only 2 not chiming at the true time. In the 3rd case, it is only one which is not chiming at the true time. And in the 4th case all are chiming at the true time.

So in any of the 4 cases, you can easily retain two of the clocks chiming at true time and the remaining 3 of the clocks could be separated and kept away.