Problem 18 · 2011 Math Kangaroo
Hard
Logic & Word Problems
clock-calendarcareful-counting
How often in a day does a digital clock display four identical digits? The picture shows a digital clock that is displaying exactly two different digits.
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Answer: C — 3 times
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Hint 1 of 2
A digital clock shows HH:MM on a 24-hour day — list when all four digits are equal.
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Hint 2 of 2
The hour can be at most 23, so check which single repeated digit even fits.
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Approach: check each repeated digit
- All four digits the same means a time like dd:dd. The hour part dd must be a valid hour (00–23).
- That allows 00:00, 11:11 and 22:22 only (33:33 etc. are not real times).
- So it happens 3 times a day, answer C.
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