Bite-sized brain teaser to solve in a minute or less.
The Mysterious Vault Code
The vault at the local museum requires a 4-digit code to unlock. The code consists of four distinct digits (1 to 9), and you have the following clues:
- The sum of all four digits is 18.
- The second digit is twice the first digit.
- The fourth digit is 5 more than the second digit.
- The third digit is larger than the fourth digit.
What is the vault’s 4-digit code?
Solution
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a + b + c + d = 18 b = 2a d = b + 5
a + b + c + d = 18 a + 2a + c + (2a + 5) = 18 5a + c + 5 = 18 5a + c = 13
From Clue 3, b is 5 less than d So, between 1-9, b can only be 1, 2, 3, or 4 But since, from Clue 2, b = 2a So, between 1-9, b can only be 2 or 4 Then a has to be either 1 or 2
If a = 2, b = 4, and d = 9 5a + c = 13 5(2) + c = 13 10 + c =13 c = 3 From Clue 4, c > d, so these values cannot be correct
If a = 1, b = 2, and d = 7 5a + c = 13 5(1) + c = 13 5 + c = 13 c = 8 And so, a + b + c + d = 18 1 + 2 + 8 + 7 = 18
The 4-digit code is 1287. |
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