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# Combination Lock

• Molly Mae
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• in post #2
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## Question

Here's an easy-ish one...

This combination lock uses digits 0-9

-[?]-[?]-[?]-[?]-

1. The first digit is a prime number.

2. The second digit is not a factor of 12.

3. The third digit is greater than the second digit.

4. The fourth digit is one greater than another digit.

5. There is exactly one odd digit.

6. No two digits are the same.

What is twice the sum of the digits?

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## 9 answers to this question

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1. The first digit is a prime number.-- 2, 3, 5, 7

2. The second digit is not a factor of 12.-- 5, 7, 8

3. The third digit is greater than the second digit.-- 6, 7, 8, 9

4. The fourth digit is one greater than another digit. -- 3, 4, 6, 7, 8, 9

5. There is exactly one odd digit.

6. No two digits are the same.

The second or third digit must be the odd one, so the first number must be 2. The second number must be 5--can't be 7+ because two numbers must be higher than it and not odd. The third digit must be > 5 but even (leaving 6 and 8). Not 6 because that would make the last digit odd. Third must be 8 and fourth must be 6.

2 - 5 - 8 - 6

42 is twice the sum of the digits.

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oops read 4 wrong but it still works

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42

by (1), (2), (5) and (6), the first two digits are in this set: 25, 27, 28, 29, 38, 58, 78

(3) rules out 29

(3) and (4) together rule out 78 25, 27, 28, 38, 58

All combinations obeying (3) and (5): 256, 258, 278, 289

all combinations matching (4): 2563, 2567, 2583, 2586, 2589, 2783, 2789, 2893

removing (5) violators 2586

sum of digits = 21, twice that is 42

Edit: looks like I got here late. Gotta remember to refresh the screen before posting (note to self...)

Edited by CaptainEd

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wel.. mutiple possibilities. or multiple Qs

2083.. 0 is an even no and 0 is not a factor of 12 and for that matter any number..... so twice the sum of digits will be 26

Edited by hhh3

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The combination -7-0-6-8- giving 42 as twice the sum also works. So does -2-0-3-4- giving 18 as twice the sum. There are others which have 0 as the second digit.

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42. The combo I found was 2 5 8 6, their sum is 21, twice that is 42.

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MM got it in post #2.

In working out the puzzle, 0 vanished from #2's possibilities in an earlier form of the rules and I must have forgotten to return it. Sorry for the confusion.

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the number is 2586 which adds nd doubles to 42

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