Bite-sized brain teaser to solve in a minute or less.
The Mysterious Lockbox
In her grandmother's dusty attic, Jenna stumbles upon an old lockbox with a strange combination lock. There are four dials, each labeled with the numbers 0 to 5. To unlock the box, Jenna must enter the correct four-digit code.
She notices a faded note nearby with the following clues:
- The first digit is twice the third digit.
- The second digit is one less than the third digit.
- The sum of all the digits is 12.
Using these clues, can you help Jenna figure out the correct four-digit code to unlock the mysterious lockbox?
Solution
| Jenna may only use the numbers 0, 1, 2, 3, 4, 5 to open the lockbox.
Let's denote the four digits as abcd, where a, b, c, and d represent the first, second, third, and fourth digits, respectively. Using Clue 1: a = 2c, so either a = 2 and c = 1, or a = 4 and c = 2 Using Clue 2: b = c-1, so if c = 1 then b = 0, or if c = 2 then b = 1 Using Clue 3: a+b+c+d = 12 If a = 2, b = 0, c = 1, then 2+0+1+d = 12, d = 12-3 = 9 If a = 4, b = 1, c = 2, then 4+1+2+d = 12, d = 12-7 = 5 Since the lockbox is limited to the numbers 0, 1, 2, 3, 4, 5, the last digit (d) cannot be 9. So, a = 4, b = 1, c = 2, d = 5 The lockbox code is 4125 |
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