How many birds do domestic cats in the United States kill every year? You win if your answer is within an order of magnitude in either direction. However, you don’t actually win anything.

The answer comes from the journal Nature Communications as reported here

To reveal the answer, select the black box. (This assumes you don’t have black set as your selection color.)

“We estimate that free-ranging domestic cats kill 1.4 to 3.7 billion birds and 6.9 to 20.7 billion mammals annually.”

And now for extra credit, within an order of magnitude, how many people subscribe to the online version of the Boston Globe? Hint: It costs $3.99/week. Hint: Greater Boston’s population is about 4M. Hint: This quarter, online subscriptions rose 8%. (The answer comes from an article at BizOnline.)

28,000

By the way, I occasionally like to acknowledge that the “order of magnitude puzzle” was invented by my famous friend Paul English.

One of the security options with Android lets you sign in by dragging you finger to trace a pattern you’ve chosen on a 3×3 square numbered 1-9. The codes have to be at least 4 digits long, you can’t repeat any digit, and you can’t lift your finger off the pad. To my always-wrong intuition, that seems like it affords too few possibilities. So, your task is to guess (or, if you must, figure out) roughly how many choices there are.

[Semi-Spoilers] You start with with the following range of numbers: 1,234 to 987,654,321. That is a boatload of numbers. But you remove all the numbers that have repeated digits. For a 9-digit number, there are only 362,880 numbers (9 factorial) without repeated digits, so that’s like subtracting 100 million numbers from the mix. Our son Nathan says that it’s the same number for all the 8-digit possibilities, because 8 factorial x 9 is the same same as 9 factorial. (I’m lost. Ask him.) After you do all of them down through 4-digits, you have to subtract the sequences that have non-contiguous numbers (based on the 3×3 square). So, it’s a big number, especially since the Android UI puts in a time-out after 10 wrong tries. But it’s not an astronomical number. I’m guessing it’s under a million.

But I fully expect to be shown to be wildly wrong.

Categories: puzzles Tagged with: puzzles Date: January 11th, 2012 dw

You win an Order of Magnitude puzzle if your answer is within an order of magnitude of the right answer. On the other hand, you don’t actually win anything. So, here goes:

How many bees do you think are in a pound? (And isn’t the answer none if they’re all flying?)

How many bees per gallon?

The answer is in the comments. (Note: This is not a computation WolframAlpha can help you with.)

This is from Martin Gardner’s upcoming book (!), as reported in WordWays:

Take any nine cards from a deck. Any nine. Shuffle as much as you want.

Divide them into three piles of three, face down. Pick up any pile, look at the bottom card, and remember it.

Assemble the three piles, putting the pile you chose on top (all still face down).

Spell the number of the card you remembered. For each letter, deal one card off the top of the deck, face down. So, if it were a three of clubs, you’d spell T-H-R-E-E, resulting in a pile of five cards. If it’s a face card, spell out its name.

Put the remaining cards on top of the pile. So, if it were the three of clubs, you’d put the four remaining cards in your hand down on top of the five on the table. Pick up all nine.

Now spell “OF” the same way, putting down two cards and putting the remaining seven on top.

Now spell the suit (e.g., C-L-U-B-S) the same way. Again put the remaining cards on top.

Spell “MAGIC” the same way. Turn the “C” card over. It’ll be the one you’re remembering.

Facing a budget shortfall, the town of Andover, MA, has decided to turn off 600 streetlights, leaving 900 on. How much do you think that will save Andover per year, according to the article in the Boston Globe?

This is an Order of Magnitude Quiz, which means you win if your answer is correct within an order of magnitude. It also means, however, that there’s nothing to win.

Four logicians are having breakfast. Waitress asks — Will you all be having coffee? The first logician says “I don’t know.” Second says “I don’t know.” Third says “I don’t know.” Fourth says “No.” The waitress returns with their coffees. Who gets coffee?

It does have a solution. The solution is not a cheat or wordplay or a sort of “lightbulb” joke anything extraneous to the puzzle. For example, it’s not “None of them, because logicians drink tea” or “None, because the first three were saying, “I don’t. No.” or “None, because coffee isn’t axiomatic.”

[HINT:]: Think about how each of the logicians would answer the question if she were going to order coffee or not order coffee.

I’ll put the answer in the first comment. [Actually, I changed my mind. I’ll post the answer in a comment if no one else comments.]

Thirty years ago, we were told that we should drive 55mph (or, in Europe, 42 euros per hectare) on the highway because that was the “optimal” highway speed when it came to squeezing miles out of gallons.

What is the current optimal highway speed?

And, for extra credit, what is the optimal speed on or off the highway? If I want to get maximum miles per gallon but don’t care how fast I go, how fast should I drive? Two caveats: Yes, I know this will be different for different cars in different conditions. And, no, zero mph is not an acceptable answer, no matter how true it is.

This is a “Let’s figure out how this statement might be true” puzzle. I have an answer in mind (which you probably won’t like), but I’m more interested in the ones y’all come up with:

For the sort of run-of-the-mill yogurt â€” no fruit on the bottom â€” you buy in your average American supermarket, I believe it is true that the further you go down in the container, the more fattening it becomes.

Why might that be true? More important, in how many different ways can we take that putative fact to make it true?

While watching our local squirrel digging up the flowerpots on our porch, thinking about how much easier it would be for both of us if the stupid thing would just evolve a bigger brain, I got to thinking about how unpleasant the bigger-brain mutation would be if it didn’t come with a simultaneous bigger-skull mutation. But having both of those mutations occur at the same time seems to multiply the improbability, doesn’t it?

So, how’s it happen? Are the two sizes controlled by the same gene? Do skulls form around brains so brains don’t rattle around in them? Does it really take multiplicative random mutations? Or what?