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2011 Math Kangaroo

Problem 5

Problem 5 · 2011 Math Kangaroo Easy
Logic & Word Problems clock-calendar

My digital clock just showed 20:11. In how many minutes will it again show the digits 0, 1, 1, 2 in any order?

Show answer
Answer: C — 50
Show hints
Hint 1 of 2
You need a later clock time built from exactly the digits 0, 1, 1, 2.
Still stuck? Show hint 2 →
Hint 2 of 2
Try rearranging into a valid HH:MM that comes soon after 20:11, such as 21:01.
Show solution
Approach: find the next time using the same four digits
  1. The display 20:11 uses the digits 0, 1, 1, 2.
  2. The next valid time whose digits are 0, 1, 1, 2 in some order is 21:01.
  3. From 20:11 to 21:01 is 50 minutes.
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