### Brain Teasers

# The Winning Combination

You are in a game show with four other contestants. The objective is to crack the combination of the safe using the clues, and the first person to do so will win $500,000.

The safe combination looks like this:

??-??-??-??

A digit can be used more than once in the code, and there are no leading zeroes.

Here are the clues:

1. The third set of two numbers is the same as the first set reversed.

2. There are no 2's, 3's, 4's or 5's in any of the combination.

3. If you multiply 4 by the third set of numbers, you will get the fourth set of numbers.

4. If you add the first number in the first set with the first number in the second set you will get 8.

5. The second set of numbers is not greater than 20.

6. The second number in the second set multiplied by the second number in the fourth set equals one higher than the numbers in the first set.

And get moving, I think another contestant has almost figured it out!

The safe combination looks like this:

??-??-??-??

A digit can be used more than once in the code, and there are no leading zeroes.

Here are the clues:

1. The third set of two numbers is the same as the first set reversed.

2. There are no 2's, 3's, 4's or 5's in any of the combination.

3. If you multiply 4 by the third set of numbers, you will get the fourth set of numbers.

4. If you add the first number in the first set with the first number in the second set you will get 8.

5. The second set of numbers is not greater than 20.

6. The second number in the second set multiplied by the second number in the fourth set equals one higher than the numbers in the first set.

And get moving, I think another contestant has almost figured it out!

### Answer

The combination is 71-19-17-68.From the second clue, we know that there are no 2's, 3's, 4's or 5's in any of the sets. Therefore, only 1's, 6's, 7's, 8's and 9's could be in the remaining spots.

Clue 3 says if you multiply 4 by the third set of numbers you will get the fourth set of numbers. From this, you can tell a 1 is the first number in the third set - any other number would be too high.

11 * 4 = 44

16 * 4 = 64

17 * 4 = 68

18 * 4 = 72

19 * 4 = 76

Of these, 17 * 4 and 19 * 4 are the only ones that are possible; as the answer of the other numbers contains a number which we know is not in the combination.

Now we skip all the way to clue 5, which tells us the second set of numbers is not greater than 20. This means that the first digit of that set is also a 1.

So far, we know this much:

??-1?-1?-??

Now, we can come to clue 4, which tells us if you add the first number in the first set with the first number in the second set you will get 8. The first number in the second set is 1, so the first number in the first set must be 7. Since the first clue tells us the first set is the third set reversed, and we know that a 1 is the first number in the third set, a 1 must be the second number in the first set and a 7 must be the second number in the third set.

So far, we know this much:

71-1?-17-??

Now, the third set (17) multiplied by 4 will get us 68. Now we know the fourth set is 68.

71-1?-17-68

Now we come to the final clue. This tells us the second number in the second set (unknown) multiplied by the second number in the fourth set (8) equals one higher than the numbers in the first set. We know that the first set is 71, so adding one to that (72) and then dividing it by 8 will get us 9. So, the finished combination is:

71-19-17-68

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