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Last winter I found myself locked out of my house because I couldn’t remember the 5 digits code to open the garage door. I used the following facts to get inside.

1. The second and third digits add up to 9.
2. The first digit is equal to the second digit cubed.
3. The sum of the third and fifth digits is the smallest number with exactly five divisors.
4. The fourth digit is equal to 6 times the second-to-last digit.
5. None of the digits repeat.

What was the code?

SherlockHolmes Expert Asked on 4th April 2016 in

82709

Yodha Expert Answered on 4th April 2016.

11864

Harsha Starter Answered on 9th April 2016.

82705

begineer Scholar Answered on 16th August 2016.

82709

If we label each digit a, b, c, d and e, we get the following equations.
1. b + c = 9
2. a = b3
3. c + e = 16 (since 16 is the smallest number with five divisors – 1, 2, 4, 8 and 16).
4. d = 6 * d (The fourth and second-to-last digits are the same number, meaning d must be zero to satisfy the equation)
5. b must be zero, one or two (b can’t be three because that makes a=27, which isn’t a single digit). Zero and one result in duplicate digits (00907 and 11808 respectively) so the only remaining value for b is 2, giving us 82709 and warmth.

SherlockHolmes576 Curious Answered on 29th April 2019.

82703

7 + 3 = 10 which is exactly divisible into 5 pieces.

Bala Default Answered on 4th April 2016.

Who the hell ? 10 have 4 divisors you. Who marked this as best is surely dumb?

on 4th April 2016.

82709 was marked as best, may be due to some mismark 82703 marked as correct

on 4th April 2016.

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