I just read an article about interviewing at Google and they gave 5 sample questions. They were hard, and made you REALLY think. Give it a try! Don't scroll down to the answers until you give it a shot!
1. What's the next number in this sequence: 10, 9, 60, 90, 70, 66 …
?
2. You're in a car with a helium balloon on a string that is tied to the
floor. The windows are closed. When you step on the gas pedal, what happens to
the balloon—does it move forward, move backward, or stay put?
3. Using only a four-minute hourglass and a seven-minute hourglass,
measure exactly nine minutes—without the process taking longer than nine
minutes.
4. A book has N pages, numbered the usual way, from 1 to N. The total
number of digits in the page numbers is 1,095. How many pages does the book
have?
5. A man pushed his car to a hotel and lost his
fortune. What happened?
OK, the answers are below.........
1. Spell the numbers out:
Ten
Nine
Sixty
Ninety
Seventy
Sixty-six
They are in ascending order, based on the number of letters in the
spelled-out numbers. A correct response will have nine letters: 96, for
instance. A cleverer answer is "one googol." That's the huge number that can be
written as a "1" with a hundred zeros after it. Google, the company's name, was
originally a misspelling of "googol."
2. The near-universal intuition is that the balloon leans backward as you
accelerate. Well, the intuition is wrong. Your job is to deduce how the balloon
does move and to explain it to the interviewer.
One good response is to draw an analogy to a spirit level. For the not so
handy, a spirit level is the little gizmo carpenters use to make sure a surface
is horizontal. It contains a narrow glass tube of colored liquid with a bubble
in it. Whenever the spirit level rests on a perfectly horizontal surface, the
bubble hovers in the middle of the tube. When the surface isn't so level, the
bubble migrates to the higher end of the tube. The takeaway here is that the
bubble is simply a "hole" in the liquid. When the surface isn't level, gravity
pulls the liquid toward the lower end. This pushes the bubble wherever the
liquid isn't— toward the opposite end.
Untie the helium balloon and let it hit the moonroof. It becomes a spirit
level. The balloon is a "bubble" of lower-density helium in higher-density air,
all sealed in a container (the car).
Gravity pulls the heavy air downward, forcing the light balloon against the
moonroof.
When the car accelerates, the air is pushed backward, just as your body is.
This sends a lighter-than-air balloon forward. When the car brakes suddenly, the
air piles up in front of the windshield. This sends the balloon backward.
Centrifugal force pushes the air away from the turn and sends the balloon toward
the center of the turn. Of course, the same applies when the balloon is tied to
something; it's just less free to move. The short answer to this question is
that the balloon nods in the direction of any acceleration.
3. Start both hourglasses at 0 minutes. Flip over the four-minute glass when it
runs out (at 4:00); ditto for the seven-minute glass (at 7:00). When the
four-minute glass runs out the second time (at 8:00), the seven-minute glass
will then have one minute of sand in its lower bulb. Flip the seven-minute glass
over again and let the minute of sand run back. When the last grain falls, that
will be nine minutes.
4. Every page number has a digit in the units column. With N pages, that's N digits
right there. All but the first 9 pages have a digit in the tens column. That's N
- 9 more digits.
All but the first 99 pages have a digit in the hundreds column (accounting
for N - 99 more digits).
I could go on, but not many books have more than 999 pages. A book with 1,095
digits in its page numbers won't, anyway.
This means that 1,095 must equal:
N + (N - 9) + (N - 99).
This can be simplified to:
1,095 = 3N - 108.
That means that 3N = 1,203, or N = 401. That's the answer, 401 pages.
5. He was playing Monopoly.
