PK 2015 Q15
15. How many three-digit numbers are there in which any two adjacent digits differ by 3?
- A 12
- B 14
- C 16
- D 18
- E 20
Pink Kangaroo 2015, Question 15. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 20
The first digit can be anything from 1 to 9. Where possible, we can reduce this by three or increase it by three to get the next digit, giving the following possibilities for the first two digits: 14, 25, 30, 36, 41, 47, 52, 58, 63, 69, 74, 85, 96. Repeating for the third digit, we obtain the possibilities in numerical order: 141, 147, 252, 258, 303, 363, 369, 414, 474, 525, 585, 630, 636, 696, 741, 747, 852, 858, 963, 969, which is 20 options.
Solution © UK Mathematics Trust, from the PK 2015 solutions.