Bite-sized brain teaser to solve in a minute or less.
The Garden Gate
While exploring an enchanted garden, Lucy finds a locked gate with a peculiar combination lock. There are four dials, each labeled with the numbers 0 to 6. To open the gate, Lucy must enter the correct four-digit code.
Nearby, she finds a plaque with the following clues:
- The sum of all the digits is 14.
- The first digit is three times the second digit.
-
The third digit is two less than the second digit.
Using these clues, can you help Lucy figure out the correct four-digit code to unlock the enchanted garden gate?
Solution
| These numbers may be used to open the lock: 0, 1, 2, 3, 4, 5, 6
Let's denote the four digits as abcd, where a, b, c, and d represent the first, second, third, and fourth digits, respectively. Clue # 1: a + b + c + d = 14 Clue # 2: a = 3b, so either a = 3 and b = 1, or a = 6 and b = 2 Clue # 3: c = b-2. If b = 1, then c = -1. If b = 2, then c = 0. Since negative numbers are not an option, c = 0. As a result, b = 2 and a = 6 Using clue # 1: a + b + c + d = 14 6 + 2 + 0 + d = 14 d = 14 - 8 d = 6 The correct four-digit code is 6206 |
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