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Vandaag is het 23 September 2017

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Mirror mirror on the wall - logic puzzle

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Matthew leaves home in the morning to go to school. At the moment he leaves the house he looks at the clock in the mirror. The clock has no number indication and for this reason the boy makes a mistake in interpreting the time (mirror-image). Just assuming the clock must be out of order, Matthew cycles to school, where he arrives after twenty minutes. At that moment the clock at school shows a time that is two and a half hours later than the time that Matthew saw on the clock at home.

At what time did he reach school?

Explanation

The difference between the real time and the time of the mirror image is two hours and ten minutes (two and a half hours, minus the twenty minutes of cycling). Therefore, the original time on the clock at home that morning could only have been five minutes past seven: 7:05 and 4:55

The difference between these clocks is exactly 2 hours and ten minutes (note that also five minutes past one can be mirrored in a similar way, but this is not in the morning!).

Conclusion: The boy reaches school at five minutes past seven plus twenty minutes of cycling, which is twenty-five minutes past seven!.