Breaking Into Luggage

After a few hours, David finally arrived at his hotel. When he wanted to open his briefcase; he couldn't remember the 4-digit combination code. He was, however, able to recall:

  • The 1 st 1^\text{st} digit is a number between 2 and 6 inclusive.
  • The 2 nd 2^\text{nd} digit is a prime number between 2 and 9 inclusive.
  • The 3 rd 3^\text{rd} digit is a number between 5 and 8 inclusive.
  • The 4 th 4^\text{th} digit is an odd number.

What is the total number of possible combination code to the briefcase?


The answer is 400.

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2 solutions

Billy Lorenzo
Mar 8, 2016

For each digit, find all possibilities.
- 1st digit = 2,3,4,5,6 = 5 numbers;
- 2nd digit = 2,3,5,7 = 4 numbers;
- 3rd digit = 5,6,7,8 = 4 numbers;
- 4th digit = 1,3,5,7,9 = 5 numbers.
And then, multiply them. 5x4x4x5 = 400.


Achille 'Gilles'
Mar 19, 2016

Answer is 400

✔ 1st number could be 2, 3, 4, 5 or 6 (5 possibilities)

✔ 2nd number could be 2, 3, 5 or 7 (...x4 = 20 possibilities)

✔ 3rd number could be 5, 6, 7 or 8 (...x4 = 80 possibilities)

✔ 4th number could be 1, 3, 5, 7 or 9 (...x 5 = 400 possibilities )

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