### Brain Teasers

# The Winning Combination 3

Well... The Winning Combination is back.. but with a twist! You are a millionaire... but you have now become very greedy and a cheater. You spend lots of money on selfish things, and are finding yourself very short of money. The show has refused to let you back on after you meanly insulted the host.

But you are sneakier than that. Now, your son has applied to be a contestant and has successfully made it on. He, however, has nowhere near the brain power as you, so you have figured out another device, being the greedy person you are, to help your son out and claim half a million more.

He is secretly wearing a very cleverly disguised earpiece which you will talk to him through. Whilst you sit at home, with a pen and paper, he will recite the clues into your ear and you must solve them for him!

You grip your pen... with headphones and microphone in place, and wait for him to start reciting.

The combination is spaced out like this... ??-??-??-??. A 'set' refers to a set of two numbers.

"OK, Dad...

1. The sum of the digits in the third set is less than 14 but greater than 10.

2. The third set of numbers is 13 smaller than the fourth set.

3. If you multiply the second set of numbers by 2 and add 7, then you will get the first set of numbers.

4. The sum of the digits in the fourth set is greater than the sum of the digits in the first set.

5. There are no 0's, 3's or 6's in the combination. Every other number is in the combination.

6. The first set of two digits is a square number (for example 81 is a square number... 9x9).

Hurry, Dad, hurry!"

But you are sneakier than that. Now, your son has applied to be a contestant and has successfully made it on. He, however, has nowhere near the brain power as you, so you have figured out another device, being the greedy person you are, to help your son out and claim half a million more.

He is secretly wearing a very cleverly disguised earpiece which you will talk to him through. Whilst you sit at home, with a pen and paper, he will recite the clues into your ear and you must solve them for him!

You grip your pen... with headphones and microphone in place, and wait for him to start reciting.

The combination is spaced out like this... ??-??-??-??. A 'set' refers to a set of two numbers.

"OK, Dad...

1. The sum of the digits in the third set is less than 14 but greater than 10.

2. The third set of numbers is 13 smaller than the fourth set.

3. If you multiply the second set of numbers by 2 and add 7, then you will get the first set of numbers.

4. The sum of the digits in the fourth set is greater than the sum of the digits in the first set.

5. There are no 0's, 3's or 6's in the combination. Every other number is in the combination.

6. The first set of two digits is a square number (for example 81 is a square number... 9x9).

Hurry, Dad, hurry!"

### Hint

The numbers in the first set are not higher than 60.### Answer

The solution is 49-21-75-88.First of all, we know that there are no 0's, 3's or 6's in the combination and that every other digit appears at least once (clue 5).

OK, we'll start on the first set.

We know it's a square number (clue 6).

The only available square numbers that don't have a 0, 3 or 6 in them are:

25

49

81

Now, read clue 3. This tells us that multiplying the second set of numbers by 2 and then adding 7 will give us the first set.

So you must work backwards from the three numbers we know are the possibilities.

81 - 7 = 74 / 2 = 37. However, we know there are no 3's in the combination so this can't be right.

25 - 7 = 18 / 2 = 9. This can't be right, because written down it would be 09 and we know there are no 0's.

So that leaves with 49.

49 - 7 = 42 / 2 = 21.

Now we know this much:

49-21-??-??

Now we must work on the last two sets.

Clue 2 tells us that the third set is 13 smaller than the fourth set.

Here are the possible combinations:

11-24

12-25

14-27

15-28

28-41

29-42

41-54

42-55

44-57

45-58

58-71

59-72

71-84

72-85

74-87

75-88

78-91

79-92

81-94

82-95

84-97

85-98

Now, we must remember clue 5 - this tells us that every number will appear in the combination at least once, apart from 0, 3 and 6.

Currently, we have 1, 2, 4 and 9 in... so that leaves out 5, 7 and 8.

So now we review the list... there are only three possible combinations that include 5, 7 and 8:

58-71

75-88

72-85

Now, we read clue 4. This tells us the sum of the digits in the fourth set is greater than the sum of the digits in the first set. The sum of the digits in the first set is 13 (4 + 9), and so the only one greater than that is the 75-88 combination (8 + 8 = 16).

So there we have it.

49-21-75-88.

(P.S. Sorry if this offended anybody, not that I think it would, but in my other teaser people were complaining so I'm just putting this in here for warning).

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