PK 2016 Q24
24. Dates can be written in the form DD.MM.YYYY. For example, today's date is 17.03.2016. A date is called ‘surprising’ if all 8 digits in its written form are different. In what month will the next surprising date occur?
- A March
- B June
- C July
- D August
- E December
Pink Kangaroo 2016, Question 24. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B June
The smallest possible first digit in the year is 2. This eliminates December from the month, leaving only months that start with 0, or 10 (11 cannot be used because it has a repeated digit). So we will definitely use 0 for the month. Not using 0 or 2 for a day leaves us with 13 to 19, or 31, all of which use a 1. Since we are using 0 and 1 for the month and day, the earliest year we could have is 2345. The earliest month is then 06, and the earliest day that can be made is 17. This gives 17.06.2345. So the month is June.
Solution © UK Mathematics Trust, from the PK 2016 solutions.