Bite-sized brain teaser to solve in a minute or less.
The Safe Code
A safe in Professor Elan’s lab is secured with a 3-digit combination lock. The digits range from 0 to 9, and Professor Elan left the following clues to help his assistant unlock it:
- The sum of the three digits is 14.
- The first digit is twice the third digit.
- The second digit is one less than the first digit.
What is the 3-digit combination to open the safe?
Solution
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Let the digits be x, y, and z: x is the first digit, y is the second digit, and z is the third digit.
From the first clue: x + y + z = 14
From the second clue: x = 2z
From the third clue: y = x − 1 or y = 2z - 1
Substitute x = 2z and y = 2z - 1 into the sum equation: 2z + (2z−1) + z = 14
Simplify: 2z + 2z − 1 + z =14 5z − 1 = 14 5z = 15 z = 3
Solve for x and y: x = 2z = 2(3) = 6 y = x − 1 = 6 − 1 = 5
x = 6 y = 5 z = 3 The 3-digit combination to open the safe is 653. |
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