Wednesday Apr 20, 2005


Here is an interesting illustration of the fuzzy pattern-matching capability of the human mind. The following paragraph contains words whose letter sequences are randomly re-ordered (except for the first and last letters). I think you'll find you can read this quite easily and quickly!

I cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was rdanieg. The phaonmneal pweor of the hmuan mnid. Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoatnt tihng is taht the frist and lsat ltteer be in the rghit pclae. The rset can be a taotl mses and you can sitll raed it wouthit a porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Amzanig huh? I awlyas tghouht slpeling was not taht ipmorant. :-)

Monday Mar 21, 2005

Competitive Takeout Conundrum

Sun Microsystems has kicked off a new sales initiative. To stimulate new revenue, 200 small but lethal "A" teams have been assigned to as many prospect accounts around the world - small but strategic/growth accounts with no Sun kit to date.

The teams were given an initial task to assess these accounts w.r.t. competitive server installed base, to help plan assault tactics. Here are the complete results of that study:

  • 104 accounts have IBM, 81 have HP, and 125 have Dell.
  • 39 accounts have IBM and HP, 58 have IBM and Dell, and 50 have HP and Dell.
  • 16 accounts have ONLY IBM and HP on their floor.

A Sigma Black Belt (an expert in SixSigma methods) was assigned to analyze the data.

How many of the accounts did the Black Belt find that did not have any servers from IBM, Dell or HP?

Sunday Mar 13, 2005

Deciphering the Data Cent

Disclaimer: I've consulted at all but one of these firms, and can tell you that this puzzle's solution does not generally describe actual purchase decisions or deployment standards at these firms. It's just a puzzle.

Your job is to figure out each firm's preferred choice of servers and storage.

  1. WalMart, the firm using SGI servers, and the firm with Hitachi storage, are all market leaders.
  2. Newsflash: CNN uses IBM servers for their back-end processing.
  3. Neither AT&T nor Disney have any AMCC storage in their data centers.
  4. The firm still using SGI uses neither NetApp nor EMC storage.
  5. Hitachi and NetApp were eclipsed on the Sun shop's preferred storage vendor list.
  6. Both WalMart and Google have kicked EMC out of their centers.
  7. Disney did not entertain the proposal to start using Fujitsu servers.
  8. A search of Google's operations shows no sign of HP or SGI.
  9. A Disney "balance-of-trade" agreement left LSI Logic without a ticket.
  10. The firm using Fujitsu servers does not permit NetApp based storage in production.
  11. Google is just starting to consider bringing in Hitachi storage arrays.

The following graphic is NOT the solution, just a randomly ordered list of related logos. It provides no useful information beyond the statements above (I just like to include a graphic with each puzzle). Good luck.

In case you give up, here is the solution:

Thursday Mar 10, 2005

24 Skidoo

Kevin Chu, of Sun Blog fame, posted a tricky little problem. I'm glad I didn't get this one in an interview!! Don't read the comments attached to Kevin's posting, unless you want to spoil the suspense. If you can't figure it out right away, go do something else. I've often put something down (a computational algorithm, a difficult musical passage on my sax, what appears to be a difficult decision, etc) only to come back to it and the solution or resolution falls right into place. I'm convinced our brains fire off low-priority background threads to ponder unresolved issues. Give it a try. UNIX systems average about 10% utilization. Same with the human brain, according to some researchers. Maybe background processing is consuming some of the spare cycles?

This problem is as easy as it sounds. No tricks at all. You must use all four integers exactly once [1, 3, 4, 6]. You may use each of the four basic arithmetic operators [add, subtract, multiply, divide], and parentheses, as many times as you wish (zero or more times). No other operators are allowed. You should end up with a simple formula that results in exactly 24. Integer math isn't allowed (eg: 6\*4 + 1/3), where 1/3 is truncated to the integer: zero. Good luck!

Monday Mar 07, 2005

Riverboat Race

This is yet another kind of puzzle. Really it's just a math problem, with a twist (not a trick, just a legitimate technique that isn't immediately obvious to most). It does rate as a puzzle (to me) because it appears quite easy at first. But once into the problem, some will think that I have not provided enough information. Good luck!

Two boats on opposite shores of a river start moving toward each other at a constant but different speeds. Neglect all other factors, such as wind and current speed, etc. When they pass the first time they are 700 yards from one shoreline. They each continue to the opposite shore, turn around (instantly) and start moving toward each other again. When they pass the second time they are 300 yards from the other shoreline. How wide is the river?

If you give up, here is the solution:

Head Start Hare

This isn't really a puzzle... But it makes for an interesting thought exercise for those who look at the trees rather than the forest.

A turtle and a hare decide to have a race. The turtle has finally figured out a way, he thinks, that will guarantee him a win, or at least not a loss. And, if he has figured it correctly, it doesn't matter how fast the hare can run! The only stipulation is that he has to have a head start... Here's his thinking:

Say the turtle gets an X minute head start, and travels at Y miles/hour. Then the hare takes off at Z miles/hour (Z >> Y). Here's the idea... After a few moments, the turtle gets to point "a". The hare, of course, takes some amount of time to catch up to point "a". But by then, the turtle has gone a bit further, to point "b". The hare will take some finite amount of additional time to get to point "b". By then, the turtle will have moved on to point "c". Etc, etc, etc....  It appears, to the turtle, that the hare will never catch up!

Clearly, the turtle is a little "slow". We know the hare will win give reasonable values for speed, race distance, and the head start. Using simple math, we can figure out the point that the hare overtakes the turtle. So, where did the turtle go wrong in his thinking?

Tuesday Mar 01, 2005

Monty's Mischief

Don't be fooled by the apparent simplicity. You've been warned :-)

Monty tells you that behind the three curtains are hidden two booby prizes and one desirable prize. Since you won the game show's challenge, you get to pick! You figure you've got a ~33% chance of winning, so you randomly pick a curtain and cross your fingers. Vanna's twin sister walks over to the curtain of your choice and is about to reveal your prize. Your heart is racing. Then Monty stops her and asks if you're sure about your choice. In fact, he'll help you out! He tells Anna to open one of the other curtains. That one contains a goat! Now, asks Monty, do you want Anna to open your original curtain, or do you want to switch? What should you do? Does it matter?

In case you give up, here is the solution:

Monday Feb 28, 2005

Puppy Perplexity

Here is yet a different kind of puzzle. It will teach you (if you figure it out) how to solve another large class of logic puzzles. Enjoy. It isn't as easy as you might think!

Your Yellow Lab Retriever is having puppies!! You (Bill) watch as she quickly delivers two males. You run upstairs to grab your camera and the doorbell rings - two of your friends (Joe and Bob) have come over to visit. You mention that your dog has just given birth. After a little while you all go downstairs to see how the they are doing. On the way down, you mention to Joe (Bob doesn't hear) that there are two male puppies. When you return, a third has been born... a chocolate!! You now have one of each color. The yellow and black lab puppies (your friends don't know in which order they were born) tumble over each other and Joe notices that those two are boys. You challenge each other: What is the probability that all three puppies are male? Bob overhears the challenge, but he doesn't know the gender of any of the puppies.

Bill, Joe, and Bob all happen to be taking "Statistics 101" together at the local community collage. Over a beer they jot down their answers. They are all pretty bright students (assume they get it right) and competitive (they don't help each other or compare notes). What did they come up with?

If you give up, here is the solution:

24K Pipe & the Banana Slug

Here is an interesting little puzzle. It isn't so much a puzzle as a highly counter-intuitive reality. If you run the math to check your assumptions, you might think you've been hit by the Intel Processor computation bug. :-)

To help you out, the average radius of the Earth is about 3,959 miles, and the classic formula is: "circumference = 2 \* pi \* radius", where "pi" is approximately 3.14156. Polar (3,949.8 mi) and Equatorial (3,963.2 mi) radii are close enough to assume a perfect (smooth) sphere for this problem.

Your company has just completed a massive global engineering project. You've built a particle
accelerator, a superconducting supercollider that circumnavigates the globe! A perfectly circular hollow pipe thru which protons and anti-protons are accelerated and smash into each other.

But just before you flip the switch to energize the superconducting magnets, the UN caves to the protest of environmentalists. Seems your pipe is hindering the migration of the
revered Banana Slug in the forests adjacent to Santa Cruz (apparently there are a lot of laywers there with nothing better to do, except maybe sue IBM). You are commanded to raise the level of the pipe by 3 feet. Since the shape must remain a perfect circle, you must raise the pipe by this much around the entire length of the 24,850 mile pipe, not just there in Santa Cruz.

Try to guess the length of the segment of pipe you will need to add to raise the level of the supercollider by 3 feet around the entire circumference of the globe (multiple choice). After you've made a guess, go ahead and run the math.

  1. More than 5,000 feet
  2. 1,000-2,000 feet
  3. 100-200 feet
  4. Less than 20 feet

Extra credit: What if you wanted to "raise" by 3 feet a circular pipe with a radius equal to the distance between the Sun and Neptune (average radius = 2,798,842,261 miles)?

In case you give up, here is the solution:

Friday Feb 25, 2005

A Pirate's Booty

Keith McGuigan posted a great puzzle on his blog. I liked it so much had to add it to my collection. If you enjoy logic puzzles, be sure to visit Keith's blog, as he will be posting new challenges now and then. Like the "3 bulb" puzzle I posted earlier, there is a "key" approach that unlocks this problem that you'll find useful in attacking other puzzles. Good luck!

Five greedy pirates follow a treasure map to a deserted island. They dig at the "X", and uncover 100 gold coins! The pirates are unionized and therefore seniority rules. However, they are also democratic, and the majority has veto and execute (as in: "off with his head") power... so the leader (the most senior pirate) must be careful.

The leader gets to decide how to divide up the booty amongst himself and the rest of the pirates. However, after the plan is presented, all the pirates (including the leader) votes on the plan. If less than 50% approve the plan, the leader is fed to the fish and the process repeats itself with the next most senior pirate.

Now, the pirates are all pretty smart and don't make rash or emotional decisions. All of the pirates use the following priorities (in the following order) to drive their voting:

  1. They don't want to get killed
  2. They want to get the most money possible
  3. They want to kill other pirates

So, how does the leader divide up the treasure such that he keeps as much as he possibly can for himself, and still survivie?

If you give up, here is the solution:
<check back soon>

3 Bulbs, 1 Trip

This one requires some out-of-the-box thinking, but still, there is no "trick". Solving this one will give you insight into an approach for a large "class" of logic puzzles - questioning assumptions and using residual data. Good luck.

You have three light switches by the front door downstairs. These are tied to three bulbs down in the basement. You have no clue which switch controls which bulb. You can't see the bulbs from the front door. Thankfully, you do know that toggling each switch "up" turns one of the three bulb.

You are lazy, or maybe just self-challenging. Regardless of your motivation, you think there has got to be a way to figure out which switch controls which bulb with a single trip to the basement.

Again, there aren't any cute tricks... You can't count on the switches being ordered similar to the bulbs. You can't see or access the wires. You have no helpers or remote cameras or anything like that.

But, taking one trip down to the basement (while you're still down there) you can tell which switches control which bulbs! How?

If you give up, here is the solution:

Tuesday Feb 22, 2005

HARD: 12 Balls and a Scale

I found it! This logic puzzle appears simple. But when I was challenged with this about 12 years ago (by my good friend Scott Bardsley - now a chip designer at Analog Devices) it took me two days to figure it out! There are no tricks. Yes, there is a solution... I do really mean three (3) moves. And the solution must work in the general case (every time). Don't start this unless you have some time (eg: flying across the pond).

You are given 12 billiard balls that all appear identical in color, size, weight, texture, composition, etc.  But one of the balls is either slightly lighter or slightly heavier than the other 11. You have a simple balance scale. Describe the process that will allow you to determine which ball is different, and if it is heavier or lighter. Oh... you can only use the scale THREE times.

In case you give up, here is the solution:

Saturday Feb 19, 2005

The Boat & The Bowling Ball

My dad sent me this logic puzzle... It isn't that hard, but takes some thought. Don't answer too quickly!

Say you're in a small row boat on a lake. Inside the row boat is a bowling ball. You take the bowling ball and throw it over board. It sinks down to and settles on the sandy bottom of the lake.

Question: If we had measured the level of the lake before the ball was thrown over board, and again after the ball settled on the bottom of the lake, would we have found that the level of the lake increased, decreased, or remained the same?

In case you give up, here is the solution:

Microsoft's Puzzle: A Challenge

If you enjoy solving puzzles and word problems you might enjoy reading the book called:

How would you move Mount Fuji?

This book contains a collection of various types of logic puzzles, design question, estimation challenges, and choice dilemmas that, according to the author, Microsoft (and others) use during interviews with new grads. The theory is that since these folks don't have a lot of industry experience or a proven track record of success, that creative thinking under pressure (a critical success factor) can be determined to some extent by observing a candidate's process of dealing with a challenging scenario to which they haven't previously been exposed.

To me, these kinds of problems provide for a fun distraction now and then.

I'm pretty good these these, but here's one that got me. Sometimes the apparently simple ones are the hardest because you can convince yourself of the one-true-answer and can't see beyond your solution. Give it a try!

How many distinct points are there on the surface of the Earth from which you can walk one mile due South, then one mile due East, and then one mile due North, and end up at the same exact spot from which you started?

It isn't a trick question, per-se. Use basic assumptions, such as walking on the surface of (not thru) the Earth, that magnetic and true North are the same, that the Earth is a smooth perfectly  spherical "globe", etc. Don't make it harder than it is. According to the book, you'd be disqualified from further consideration for a job at Microsoft if you came up with "zero" or "one" point.

In case you give up, here is the solution:




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