I bought a car with a peculiar 5-digit-numbered licence plate that could still…
2023
I bought a car with a peculiar 5-digit-numbered licence plate that could still be read when turned upside down. When reversed (turned upside down), its value decreased by 78,633. If all the digits were different, what was the original number?
- A.
10968
- B.
89601
- C.
98601
- D.
89610
Attempted by 4 students.
Show answer & explanation
Correct answer: B
When a numeric plate is rotated 180 degrees, only the digits 0, 1, 6, 8, and 9 stay readable: 0, 1, and 8 look identical upside down, while 6 and 9 swap into each other. The rotation also reverses the order of the digits — the digit that was last becomes first (after being flipped), and so on. So for a 5-digit original number N (all different digits, each from the set 0, 1, 6, 8, 9) whose rotated reading is R, the question's ‘decreases by 78,633’ condition means N − R = 78,633, with N necessarily the larger of the two readings.
Digits of 89601 are 8, 9, 6, 0, 1 — all from the flip-safe set (0, 1, 6, 8, 9) and all different, so it is a valid plate number.
Reverse the digit order: 1, 0, 6, 9, 8.
Flip each digit in place (6 becomes 9, 9 becomes 6, others unchanged): 1, 0, 9, 6, 8 — so the rotated number is 10968.
Subtract: 89601 − 10968 = 78,633, which matches the decrease stated in the question.
Testing the value 89601 against this rule: since it is the larger of the pair {89601, 10968} and their difference is exactly 78,633, it satisfies both the digit-validity condition and the ‘decreases on reversing’ condition. Reading the plate the other way round (starting from 10968) would make its rotated reading (89601) the larger one, so reversing would increase the value — contradicting the question — which rules that ordering out.