A director of staffing at Microsoft says he asks potential employees this question:

If you have a fishbowl with 200 fish and 99 percent are guppies, how many guppies do you need to remove to get to the point where 98 percent of the remaining fish are guppies?

ANSWER: 100. (Microsoft still uses this question, so while they're willing to tell us the answer, the solution is still top secret.)

More interview questions, excerpted from 'How Would You Move Mount Fuji: Microsoft's Cult of the Puzzle -- How the World's Smartest Companies Select the Most Creative Thinkers,' by William Poundstone:


QUESTION 1: There are three ants at the three corners of a regular triangle. Each ant starts moving in a straight line toward another, randomly chosen corner. What is the probability that none of the ants collide?

ANSWER: One in four. Each ant can only move in two directions. Multiply that to get the total number of possibilities (2x2x2=8 ways). There are only two ways the ants can avoid running into each other. Either they all travel clockwise, or they all travel counterclockwise. Otherwise, there has to be a collision.

Pick one ant and call him "Bill." Once Bill decides which way to go (clockwise or counterclockwise), the other ants have to go in the same direction to avoid a collision. Since the ants choose randomly, there is a one-in-two chance the second ant will move in the same rotational direction as Bill, and a one-in-two chance the third ant will. That means there is a one in four chance of avoiding a collision.


QUESTION 2: Suppose you have eight billiard balls. One of them is defective -- it weighs more than the others. How do you tell, using a balance, which ball is defective in two weighings?

ANSWER: A balance is a simple two-pan set-up, like the blindfolded figure of Justice holds. It tells you which of the two pans is heavier, though not by how much. It can also tell you when the two pans are of equal weight.

The obvious approach will not work. That would be to weigh four balls against four balls. The heavier pan would have to contain the defective ball. Split that group's balls into two pairs and weigh the pairs against each other. Again, the heavier pan has to contain the defective ball. You’re then out of your two allotted weighings. There is no way to decide which of the two suspect balls is heavier.

The solution is to make full use of the fact that the balance can tell you if two pans are equal. Whenever the two pans are of equal weight, you can conclude the defective ball is not in either pan.

For the first weighing, pick any three balls and weigh them against any other three balls. This has two basic outcomes.

One is that the balance finds the two pans equal. In that case, the defective ball must be one of the two you didn’t weigh. For the next and last weighing, just compare the two so-far-untested balls. The heavier one has to be the defective ball.

The other possible outcome of the first weighing is that the balance finds one of the two pans heavier. The defective ball must be in the heavier pan. For the final weighing, pick any two of the balls in the heavier pan and compare them. If one is heavier, it’s the defective ball. If both are equal, the defective ball has to the third ball that you didn’t weigh this time.

This puzzle is known throughout the world. It appeared, for instance, in Boris Kordemsky’s Mathematical Know-How (1956), the best-selling puzzle book of the Cold War Soviet Union.


QUESTION 3: If you could remove any of the 50 states, which would it be? Be prepared to give specific reasons why you chose the state you did.

ANSWER: Popular answers: Alaska, Hawaii, North Dakota

Bad answer: Washington

Worse answer: I’d remove all of them.

This is Microsoft’s most notorious example of an ill-structured problem. It is not like asking for your favorite color. They want you to re-frame the question so that it has a "right answer" you can determine by logic.

You don’t have to name the state up front. You can walk the interviewer through your reasoning and decide the state at the end of it. Here is a composite and elaboration of approaches that have met with approval:

The central issue is, what happens to the people in the "removed" state? Are we nuking the state? Let case (a) be that when you "remove" a state, you are killing all the people in it. Then there is a moral obligation to minimize casualties.

Case (b) is that the state’s people just disappear. They’re not actually killed, they’re just gone. Maybe it’s like going back in time and stepping on a butterfly, then returning to the present to find that the state and its people don’t exist and never did. All the flags have 49 stars, and there is no mention of the removed state in any encyclopedia.

Case (c) is that only the real estate vanishes. The people are left behind, as homeless refugees sitting next to a gaping hole in the ground and wondering where they’re going to sleep tonight. The people will be relocated at staggering cost (to Microsoft? to the federal government?).

Case (d) is that the people are "magically" relocated, at no emotional or financial cost to anyone. Push the button, and the ex-state’s ex-residents all have homes and jobs somewhere in the remaining 49 states (assuming they had them before) and without displacing anyone in those 49 other states.

Case (e) is that no one, and no real estate, vanishes. The "removal" is purely political. The removed state becomes part of Canada or Mexico. Or it becomes an independent nation.

The choice in case (a) is clear enough. People are being killed, so you have to pick the state with the smallest population. In the 2000 census, that was Wyoming.

Case (b) is a tough call. People just vanishing is an entirely hypothetical situation without any moral precedents. Still, the people are living, breathing souls until you hit the history-eraser button. That seems tantamount to killing them. Again, the choice should probably be Wyoming.

The dilemma in case (c) is whether to consider removing a more populous state than Wyoming, in view of Wyoming’s natural attributes. Wyoming is a big state with beautiful scenery and Yellowstone National Park. To save all that, you might be willing to pay for the higher relocation costs involved in removing a more populous (but smaller and/or less scenic) state.

By the 2000 census, the five least populous states are Wyoming, Vermont, Alaska, North Dakota and South Dakota. Vermont and Alaska also have spectacular scenery, and Alaska is huge. South Dakota has Mount Rushmore. North Dakota -- well, North Dakota doesn’t have Mount Rushmore. It stands out as the only state where it’s hard to imagine anyone from another state intentionally taking a vacation there. (The joke is that the state tree of North Dakota is the telephone pole.) While other plains states are flat and treeless, North Dakota has the harshest winter climate -- harsher than the main population centers of Alaska.

Now in case (c), no one’s killed but we have to pay for relocating the people from the removed state. Surely it’s worth springing for somewhat higher relocation costs in order to save Yellowstone -- or the Vermont ski resorts, or all of Alaska, or Mount Rushmore. North Dakota is dispensable.

In case (d) the relocation is magical and free. That’s all the more reason to remove North Dakota.

Finally, in case (e), neither people nor real estate is lost. We just redraw the political map. There is something to be said for removing Alaska or Hawaii. Each is outside the contiguous United States. Some would say that having them as states savors of colonialism. If you are concerned mainly about the way countries look on the map, it’s probably a toss-up between Alaska and Hawaii.

Face it: Were Congress to debate which state to remove, maps would be the least of it. Alaska has oil and minerals. Hawaii is a place mainlanders like to vacation. Both states have strategic importance. That would nix any talk of ceding them.

The debate would focus, as in (c) and (d) above, on the states with smallest population and least natural resources. That would again lead to North Dakota, which is helpfully on the Canadian border. Offer it to Canada. If they don't want it, set it up as a country.

And if you haven't figured it out yet, Washington is a bad answer because it wouldn’t be wise to remove the home state of the employer, in this case Microsoft, asking the question.