This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 3

2022 HMNT, 1
Emily’s broken clock runs backwards at five times the speed of a regular clock. Right now, it is displaying the wrong time. How many times will it display the correct time in the next 24 hours? It is an analog clock (i.e. a clock with hands), so it only displays the numerical time, not AM or PM. Emily’s clock also does not tick, but rather updates continuously.
clock algebra

2019 India PRMO, 10
One day I went for a walk in the morning at $x$ minutes past $5'O$ clock, where $x$ is a 2 digit number. When I returned, it was $y$ minutes past $6'O$ clock, and I noticed that (i) I walked for exactly $x$ minutes and (ii) $y$ was a 2 digit number obtained by reversing the digits of $x$. How many minutes did I walk?
time clock algebra

1995 Swedish Mathematical Competition, 2
Botvid left home between $4$ and $5$ for a short visit to Amanda. When he came back between $5$ and $6$, he found that the hands of the clock had changed places. What time was it?
clock algebra