           ## Puzzle to waste your weekend

I'm going to do something useful for you. I'm going to post a puzzle that can get you a job at Google if you solve it. No guarantees, but they'll probably think your smart or something. The puzzle was printed in an ad in the Tech Review, though there may be other dorky magazines carrying it.

You have to guess the number that goes on the last column. To get the job you have to e-mail your resume to labjobs@google.com. (click for larger size)

No posting of answers, though hints are welcome. I don't know the solution, though I've narrowed it down to the candidate solutions.

In case you can't read the columns well, the numbers are 26, 14, 5, 2, 20, and ?.

Update: I have seen multiple people suggest in sites linking to this page that the number 20 is in the wrong place. While there may be multiple solutions, including ones that involve moving the 20, I know of a solution that works very gracefully with the numbers pictures exactly as they are in the photo. It's all a matter of how you count, and that will be my only hint on this problem.

Alex:

Well, I have one candidate based on comparing differences between successive numbers in rows (assuming there are two rows that run from the wall toward the viewer).

Ken:

There are three rows, and they run parallel to the viewer, so a solution that is based on differences coming towards the viewer is going in the wrong direction, so to speak.

Cody:

This problem just arrived in my August 2004 MENSA Bulletin. I've discovered lots of non-mathematical solutions to it, and also I've found the solution for differences in the rows that are coming towards you. I have not been able to find a good pattern for the three horizontal rows. Anyway have any clues for this solution?

Just some guy:

Hints:
Columns
5 = (3x1) + 2
+ +
(3x3) (3x6)
= =
14 + (3x2) = 20
+ +
(3x4) (3x?)
= =
26 + (3x?) = x

Just some guy:

I'm not sure you're on the right track. The most elegant solution I know of is different. Then again, yours might be better.

Sarkis Shmavonian:

This problem hints at no functional parameters for discrete operators (either inclusive or exclusive). Therefore, I say the answer is 23.

rose:

44

Clueless:

It's simple... 14 is the answer

di:

17

Virginia Rezaie:

I found the puzzle in Mensa magazine. The answer is 35. It works for progression from front to back, back to front, side to side and any combination left-right-forward and vice versa. Not being a math whiz, I can't tell you what the formula is...Will leave that to you brainy types. I'm just a writer.

44:

Where can we get or will we ever get the answer?

I know of one answer, it has been given here in the comments by one person, however, it is conceivable that there are multiple, valid answers, depending on how you justify. I doubt that Google will release what they believe to be the answer, and I do not plan to release an answer either.

Can you give the exact description of the puzzle that is printed in the magazine? I'm trying to determine the extent to which the approach needs to be tied to the photo given, or are we just looking for the most likely solution to a numerical pattern.

The picture is pretty much everything. The text next to the picture says "If you know what number goes on the last column, tell us." The rest of the text is in relation to applying for a job at Google.

The solution I believe is correct depends heavily on the photograph. Others in the comments have claimed answers that don't depend on the particulars of the photograph. I am inclined to believe the solution that does depend on the photograph, as it is a fairly elegant one that relies on math typically taught in computer science.

Tony Warren:

17

Rudy from Maine:

35

Computer science? Perhaps we don't need no stinking computer science.
There are 12 triangles in the picture.
For each triangle find the length of each side, and the underlying pattern that all the triangles obey.
Observe that all column numbers are of the form 2 + (3*n).
You do the rest.

FWIW, I'd like to think that Google Problem 1 (involving the vending machine) was to find the programmers. This one, perhaps, is to find the pattern recognizers. But then, what do I know? Maybe all the answers on this page are "right"...

Matthew:

The answer is 23 because each of the two rows coming toward the viewer adds up to 45. There is also another pattern. The 2 is 3 less than the 5, 20 is 6 greater than 14, and 23 is 3 less than 26. It just works out that way.

barry:

44

Angel Torres:

22

Chris Muse:

I think its 35 also. See the EXIT sign

Peach:

Finally Rudy, someone with the same answer as me.

Linda:

I also saw the puzzle in the Mensa bulletin - there's a pattern running around the outside of the photo/scratch area that includes the "A. Some resumes we get go straight etc..." and an arrow and some symbols. Does THAT pattern signify anything to anyone?

Anonymous:

5/2
14/20 = 7/10
26/? = 13/17

? = 34

Enrique Quintero:

Why?

Here the solution:

5 ---> (-3) ---> 2 ---> (+12) ---> 14
14 --->(-3*(-2)) ---> 20 ---> (+12/2)---> 26
26 --->((-3*(-2))*(-2))---> 14

That's it!

sfen:

44, and it's too easy to explain :-)

peej:

There is certainly more than one answer. I like 44 as the simplest pattern. Though some may think it too easy to explain, the fact that you don't explain it seems just a bit arrogant. The difference between the columns on the left is half the difference between the columns on the right.

dubya:

Obviously there are many ways to justify an answer. There are probably a number of answers. With intelligence testing, people that have similar IQ will answer questions similarly, right or wrong. They are looking for smart people and this is a way to filter them.

daavid:

I got 38.

Lisa:

From pole to pole is a multiple of 3
Starting with 1 and ending with me

Jay:

I think the answer is 41.

Reasons:
Looking at the columns horizontally,
1 - The numbers are increasing from back to front and with the exit sign in the front and pointing to the right of 26 shows me that the ? must be the largest number since it is closest to the exit.
2 - The formula to calculate the difference between columns is 9n-3. Where n = 0,1,2.
i.e. 2 = 9(0) - 3 + 5
20 = 9(1) - 3 + 14
41 = 9(2) -3 + 26
3 - All the numbers are in the form of 3n+2 and 41 meets this criteria.

Doug:

jake:

5*(3*1+1)=20
2*(3*2+1)=14
5*(3*3+1)=?
2*(3*4+1)=26

Um... I think there are any number of solutions... Couldn't all of the columns on the left add up to the total sum of the columns on the right?

Alternately, the absolute value of the difference between the left and right column increases from 3...to 6... to... 9 (6+3) or 12 (6 * 2)

This is my first 30 seconds worth on this one but at first glance I don't see a definitive distinguishing answer. Will have to check it out some more.

Jesse Mandel:

I agree with Jay, answer being 41. Along with what he says. The adjacent differences form the sequence 3,6,9,12,15,18,21 (counting by threes)

I think the answer is 35. Ga. Tech students would love to have this in our paper. This would make the Friday lectures so much better.

ZeD:

If you want to join google, just send this picture with the answer 35. Yes, 35 is the right answer.

dj42:

23. It's so obvious it causes people to overthink it. Smart puzzle.

Anonymous:

Ummm... could this just be the base 7 garage? So the answer is 32?

I surfed in on your puzzle, nice. There can be only one solution and at least the photographer and the person editing the picture know the right answer.
The number I think of is 23, it just troubles me that it doesnt fit with the lines painted on the floor, or maybe its just because the picture is not very clear for the rows far away?

James:

Here is a non-mathematical approach to this puzzle. Convert each number into a letter. i.e. 2=b, 5=e, 14=n, 20=t, 26=z, ?=any character. Unscrambling these characters while substituting ? with every letter of the alphabet will produce only one valid English word. That word is bezant (a gold coin used in the middle ages). Since the letter "a" was used to form this word, the missing number is 1.

james:

In addition to what Jay said (where the horizontal equation is y = 9n-3 + x; where n = 0,1,2...), the left vertical equation is next_x = 9 + 3n + previous_x; and the right vertical equation is next_y = 18 + 3n + previous_y. Using these three equations, you can predict what the numbers will be for additional columns. For example the columns could be as follows:
5 2
14 20
26 41
41 65 -- Hor:65=9*3-3+41,--Ver:41=9+3*2+26 & 65=18+3*2+41
59 92 -- Hor:92=9*4-3+59,--Ver:59=9+3*3+41 & 92=18+3*3+65

I think most answers were based on one equation without another to verify. For example, let y = 2x - 8 be the equation. This would result ? = 44. But there is no other equation to verify this value. Also, there is no pattern to predict what the next column values will be.

Jeetesh Khurana:

answer is 44 .... 100% sure

Kiran:

Its very simple, its just a garage with 3 parking spots between the poles. Now, the farthest row of poles have only 3 spots (toward us) because the other side is the driveway. 14 and 20 are parking spot numbers to the right of the pole and towards us. similarly, after 26...just count the parking spots.. :-)

Chris:

I've been waiting to see if Google ever posted the answer .... I got 35 too.

There are three parking spaces between the columns.

To solve the problem, multiply the row times the three spaces.

In the first row, (1 row) x (3 spaces) = the difference between 2 and 5

In the second row, (2 rows) x (3 spaces) = the difference between 14 and 20

In the third row, (3 rows) x (3 spaces) = the difference between 26 and the missing number

lilianarum:

following the pattern leads to 23

Lindsay:

Jack Veraart:

the map of the garage :

11 10 6 5 4 3 2 1
........................Enter
: 12 13 14 15 16 20 21
: 31 30 26 25 24 23 22
........................Exit
32 33 34 35 36 40 41 42

Start at 1, count octal from right to left
( 8 positions to park your car)
the 2nd row from left to right,
( 7 positions )
the 3rd row from right to left
( 7 positions )
and the last row from left to right.
( 8 positions )

There are no numbers left of 12 and 31 because you need some driving space there.

Anonymous:

Without further information the answer is 23, or the answer is 35 or the answer is a number of other values. Not enough information. Qiut wasting my time or yours.

It's 26, 14, 5, 2, 20, and 23.

Let x be the unknown.
Given, 5>2 and 14x
Also, (5-2) = (3*1) and (20-14) = (3*2).
Therefore, x may be (26-3)=23, (26-6)=20, (26-9)=17, ...
But given, 2620>2.
As a result, x can only be 23.

Or to think of it graphically:

09 08 07 06(05)04 03(02)01

-- -- 10 12(14)16 18(20)--
-- -- 11 13 15 17 19 21 --

30 29 28 27(26)25 24(23)22

pankaj kumar:

Answer is 44, too simple, lol

jason rose:

The answer is 35.The 2 and the 5 are on the wrong columns.It is very simple.You take the progression of numbers 2+12=14+12=26 next 3 columns are 5+15=20+15=35 from left to right 2+3=5 14+6=20 26+9=35.All three ways end up with the same number so it is correct thank u.I'll let myself out

Robin:

Yes, it's 44