This puzzle came via Facebook from Darla. She is not sure of its source.

Darla sees at least two logical answers and would love to hear your opinion which one is right.

4+6+8=9

8+10+12 =15

12+14+16=21

18+20+22= ?

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Darla sees at least two logical answers and would love to hear your opinion which one is right.

4+6+8=9

8+10+12 =15

12+14+16=21

18+20+22= ?

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

## 17 comments:

30 would be my guess, it appears that the previous solutions are all added and then divided by 2?!?

One answer is: 18+20+22=30

We have 4+6+8=18 and 18/2=9

8+10+12=30 and 30/2=15

12+14+16=42 and 42/2=21

Another is: 18+20+22=27

We have 9+6=15

15+6=21

21+6=27

Have a good week end!

Love your cookies'story and the result is great!

Anne-Marie

I would have to say the answer is 30. The other "answers" are actually half of the real answer. It's nice to have you back.

Gurubandhu

I've looked at this problem and have come up with 30 from three different methods. The last equation in the progression is essentially 1 1/2 times the previous equation in the progression so the answer would be 1 1/2 x 6 = 9 which would be added to 21 giving us 30. This is just one of the three ways I came up with the same answer. I've walked away from this hoping to find a different logical answer when looking at it freshly. For now this is all I've got!!

I get 30 for the last row. All the others appear to be half the sum of the 3 numbers. So, 18+20+22=60 and 60/2=30.

One answer:

18+20+22 = 30

This solution works if the units of the numbers on the left of the equations are a half unit (for example, a half dollar) and numbers on the right side of the equation are a full unit (for example, a whole dollar).

4+6+8 = 9: 18 (4+6+8) half-dollars = 9 full dollars;

8+10+12=15: 30 half-dollars = 15 full dollars;

12+14+16=21: 42 half-dollars = 21 full dollars; and

18+20+22=30: 60 half-dollars = 30 full dollars.

I'm still thinking about other possible solutions.

TracyZ

TracyZ

I have to admit from the onset that I am horrible at these things. I usually don't see any patterns in lists of numbers. So I consider myself lucky if I come up with 1 good pattern.

The one presentable pattern that I can find is this. Suppose you have

2x - 2, 2x, 2x + 2 If you add these numbers together you get 6x which when divided by 2 gives 3x. That works for all three cases whose answers you know. For example the third one gives 3*14/2 = 21 which I would consider a logical result. The fourth equation is therefore 30.

The symmetry of the givesn in each of the four equations would let any three numbers work as long as those three enjoyed the same symmetry. For example

x - 5 , x , x + 5 would still give 3*x as your answer.

The problem is that I am torturing the meaning of a plus sign and an equal sign. I am really soving not what is given, but 1/2 (4 + 6 + 8) = 9 and not 4 + 6 + 8 = 9

The only other solution I can think of is some sort of modular answer where nine represents a remainder in some mathematical system that works like a clock. But I see no common thread.

I have mulled this over for a day and come to nothing. I will submit it, but I'm not very happy with my answers or to see through it.

I await Monday morning with anticipation: I am looking forward to seeing what I have overlooked.

The most logical answer is 30, as the pattern seems to be taking the sum and dividing it by 2. I can't come up with any other reasonable ones on my own, looking forward to learning what Darla had in mind for hers "second" one.

The answer I got is that 18+20+22=30.

The sum of each set of numbers is divided by two to get the answer. 4+6+8=18, 18/2=9. 8+10+12=30, 30/2=15. Et cetera.

I actually couldn't originally see a pattern, but when I showed it to my friend, she saw it immediately.

Good morning, everyone!

In the original message Darla wrote:

There are at least two logical answers. Most people say the answer is 30, the simplest answer, by adding each line and devising the answer in half. However, from a puzzle/ pattern perspective, 29 has at least three reasons it is the more logical answer mathematically. I'd love to know your answer? I usually score high on IQ tests, which are mostly composed of puzzles like this. I chose 29 as my answer. The more popular answer by the general public is 30. Then again, the general public doesn't usually score as high as I do on IQ tests. So, I'd like to know if either answer is correct, or if only one answer is correct, and if so, which one?

Let's see:

We all agree with the 30 being an answer. The easiest way of seeing it is by adding all three numbers on the left and dividing the result by 2. This works for all the lines.

But Darla is saying that this is too straightforward and perhaps some trickier solution is assumed.

Anne-Marie proposed 27 as an additional answer. She got it by noticing that the patterns in numbers on the right: 9, 15, 21. They differ by 6 and therefore the next number could be 21+6=27

Very interesting! However, to my opinion this is not a "proper" answer as it completely disregards the left part of the puzzle.

It took me a while to see how Darla came up with 29. But her note about patterns led me to see that in the first line the last number on the left (8) differs by 1 from the number on the right (9). On the next line, the difference between 12 and 15 is 3. On the third line, the difference between 16 and 21 is 5. So, one could assume that on the next line the difference between 22 and ? should be 7. Therefore the ? is 22+7=29

It it neat. However I think this is also not a proper answer because it disregards the first two numbers in every row. I think that the most logical answer should take into account all the data we have, or the most of the data. From this perspective 30 is the best.

I will be happy to hear any other opinions.

3 puzzle points for Darla for suggesting a puzzle and puzzle point for each answer.

I saw 29 when doing this and did not submit it. The reason I didn't is because if you change the order you present the puzzle, 30 will work, 29 will not.

I believe 29 puts too many constraints on the pattern: it makes the order that the lines are presented just as important as the answer. While this may be necessary for a matrix, I'm not sure it should be necessary for a series of numbers. I'm not even sure I accept 30. Certainly the equal sign makes all 4 statements untrue. For example 4 + 6 + 8 = 18, not 9. It may be a picky point, but if may symbols are used, they have defined meanings and we need to obey them.

I think the way Darla came up with 29 for an answer is again forgetting the left side of the equation, not looking at the entire equation and progression. Each new line begins with the last number of the previous line which will add 4 to the last number on the left. The last equation adds 6 to the number.

16 + 18 + 20 would be the next logical line and to add 7 (as Darla would)to 20 would give 27 as the answer. The next line would be 20 + 22 + 24 = 33. This is consistent with the left and right sides of the equation and is consistent with 18 + 20 + 22 = 30.

Another way that I can see getting 29, is that if you look on the left side of the puzzle, in the first three equations, each number increases by 4 down each column (4,8,12; 6,10,14; 8,12,16) and in the last, they increase by 6 from the previous equation (14,18,22). The numbers on the right increase by 6 (9;15;21) so we could consider that the next one increases by 8 (since the pattern on the left went from 4 to 6, we assume the pattern on the left goes from 6 to 8). That would also give 29.

It will be 30.

I would look at Melissa's idea a little differently. The left side went from adding 4 to adding 6 and 6 is 1 1/2 times as large as 4. For the right side of the equation we want to do the same thing. We've been adding 6 to each number. 6 x 1 1/2 = 9. Add this to 21 for 30.

The rational answer is thus:

1.

18/3=6 +3=9

30/3=10+5=15

42/3=14+7=21

60/3=20+10=30

2.

Prime number method-1 of the value=30

17-8=9 (17-1=16/2=8)

29-14=15(29-1=28/2=14)

41-20=21(41-1=40/2=20)

59-29=30 ( 59-1=58/2=29)

3.0

+18 answer is (21)it is rational 27+18=45+18=63 +18=81

18+9=27

30+15=45 (27+18=45)

42+21=63 (45+15=63)

60+21=63 (63+18=81)

I also got 27 as best answer.

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