Maybe it's the traditionally educated engineering in me (I was trained as a mechanical engineer), but I don't see a point in this purely theoretical hand-wavy math. There are established ways for us to get good estimates of a great deal of information - including your hairdresser problem - that involve seeking out real data. Sitting in a void of zero knowledge and postulating wildly, even if it gets you in the ballpark, is wildly inefficient and I'd hate to be involved in it as part of a professional company.
A number out of your ass - regardless of how soundly backed with logic - is at the end of the day a number out of your ass. This isn't to say that all inference or estimation is bad - but rather that estimations done in a complete void of background data is practically useless.
A more concrete example: estimate the number of users our chief competitor has. I can go through this like a logic puzzle and come up with a number that has zero verifiability... or I can go look up relevant data (their page rank on Google, other available metrics on their site, etc) and arrive at a far better conclusion.
I agree with the GP that these exercises are pointless and unrelated to the job for which you are interviewing. As a traditionally educated engineer, my training teaches me not to guess whenever facts are available. Don't try to memorize and infer numbers - keep your references within reach at all times. An engineer who makes few assumptions about his data is one who makes fewer mistakes and costs less money in damage.
I don't disagree. If you actually asked me for informational purposes, I'd have started with the Yellow Pages and then go look for a trade association or something.
On the other hand, that's not always practical. Sometimes the facts aren't readily to hand or you have to make some decision that's time sensitive. For example, working in film production it's not so unusual to have to eyeball something and estimate your needs for time or material - you try to anticipate as much of that as possible in advance, but say you come to the set one day and the lead actor has fallen ill, so now you have to rearrange your shooting schedule on the fly...in which case it's not uncommon for a few key crew members to huddle, deliberate, and then split the difference rather than obsess over further optimization.
This isn't to say one should rely heavily on gut decisions, since that's likely to be self-defeating; on the other hand, you don't use a slide rule and protractor to drive.
"As a traditionally educated engineer, my training teaches me not to guess whenever facts are available."
Ah, but the most lucrative questions are about products not yet invented, for which there are few facts. They are lucrative because there is not yet any competition. If there were lots of facts available, ripe for the picking, then by definition the net margins would be terrible.
For instance, suppose you were a grad student at the MIT Media Lab in 1995. Does it make financial sense to join the work on an electronic ink product? The answer to that question could only have been derived from a series of guesses and wild deductions. You cannot just look up how efficient planar electroluminescent backlights are going to be in 10 years. Or how expensive and power-hungry non-volatile memory devices are going to be in 10 years.
For a research organization to invent and capture a new market, they have to be good at making and using wild guesses about the future. (Looking up answers is valuable too, but for different reasons.)
I think you're badly mistaking what I'm talking about with "looking up answers" - what I'm talking about is considerably more than that.
How efficient will planar electroluminescent backlights be in 10 years? That's a good question - and one we can make an educated stab at given the right historical data, the right experience in forecasting, and a little bit of plain luck. Heck, you're now talking about an entire field of mathematics and engineering in and of itself!
Compare this to the Google interview though - where they expect you to pull a number out of your ass, with no opportunity to consult historical data, no field experts to interview... no due diligence done at all. It is either an extremely poor approximation of real-life problem solving skills, or everyone at Google is recklessly cowboy and trying to deduce every decision ever by sheer will of logic alone.
A number out of your ass - regardless of how soundly backed with logic - is at the end of the day a number out of your ass. This isn't to say that all inference or estimation is bad - but rather that estimations done in a complete void of background data is practically useless.
A more concrete example: estimate the number of users our chief competitor has. I can go through this like a logic puzzle and come up with a number that has zero verifiability... or I can go look up relevant data (their page rank on Google, other available metrics on their site, etc) and arrive at a far better conclusion.
I agree with the GP that these exercises are pointless and unrelated to the job for which you are interviewing. As a traditionally educated engineer, my training teaches me not to guess whenever facts are available. Don't try to memorize and infer numbers - keep your references within reach at all times. An engineer who makes few assumptions about his data is one who makes fewer mistakes and costs less money in damage.