PK 2019 Q19
19. The integers from 1 to 99 are written in ascending order without spaces. The sequence of digits is then grouped into triples of digits:
Which of the following is not one of the triples?
- A (222)
- B (434)
- C (464)
- D (777)
- E (888)
Pink Kangaroo 2019, Question 19. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D (777)
The two-digit integers start with the pair of triples (101), (112). If we continue to consider the triples in pairs, then the following pairs start with the integers 13, 16, 19, etc. That is, they start with those integers that are 1 more than a multiple of 3. All of 22, 43, 46, and 88 have that form, they start the triples (222), (434), (464) and (888). Although 76 also has that form, it starts the triples (767) followed by (778), so that 777 is not a triple.
Solution © UK Mathematics Trust, from the PK 2019 solutions.