![How about a word problem for your Thursday evening? A classic high school mathematics word problem.
My friend Brad called me last night while I was engrossed in reading Wallace and Wallechinsky’s 1980 hippie prophecy collection The Book of Predictions — he’s one of the few people I know that will still leave a funny voicemail message, if he gets your voicemail, instead of hanging up and texting you — to get some help with this problem he was having. I don’t know why he thought I’d be good at helping him with a math problem. But I was sort of touched he thought of me. It means he thinks I am a well-rounded person. Maybe. But not with math.
The problem was this: he has a book being published by the Little Brown Mushroom imprint this month. It’s called Conductors of the Moving World, and it sounds amazing. A description:
In the autumn of 1972, a delegation of Japanese police officials visited the United States to study traffic control in several large cities, including New York, Las Vegas, and Los Angeles. The unofficial photographer for the delegation was Eizo Ota, an inspector with the law enforcement department of the Yamanashi Prefecture, and he produced a record of the group’s travels that might best be described as forensic tourism.
Using Inspector Ota’s snapshots as launching points, Brad Zellar plundered traffic manuals, haiku anthologies, the Watergate transcripts, and The Godfather for textual inspiration. The mysterious result is a Zen travelogue through 1972 America.
Now, here’s the problem. There were 51 possible photographs from Ota’s collection, 500 prints of each photograph. These 51 photos were arranged in 17 sets of 3 related images: so that’s one set of three different shots of, say, the Statue of Liberty. Same subject, three different shots. The photos are all hand-printed, and hand-tipped into each of the 500 books, and each book will get 17 of the photographs. There’s no order — the photos will be randomly placed in each book, in no particular sequence. The only rule is photos from the same 3-photo set cannot be used in the same book.
So, the problem:
How many possible iterations of the book are there, if each book has 17 photographs, with each of these photographs being 1 of 3 possibilities from 17 different groups, from the possible pool of 51, arranged in any sequence?
It took me and Brad a half-hour to even describe it to each other in that language. That still sounds clunky. So I told Brad I’d do what I’d have done in high school: talk to my dad.
Dad holds a degree in engineering from the University of Cincinnati (BEng, ‘76). Mathematics is an area in which he excels. After talking him through it, using very clunky language, and being reminded what factorials are (this one: “!”), we figured that the equation looks like this:
3^17 [that is, the number of possible combinations of the photos] * 17! [the number of possible ways in which the photos could be sequenced]
And the answer:
4.59335324 × 10^22
Or:
45,933,532,441,368,219,648,000
Or:
45 sextillion, 933 quintillion, 532 quadrillion, 441 trillion, 368 billion, 219 million, 648 thousand
Now of course, realistically, there’s only 500 different books. But there are over 45 sextillion possible configurations of this book, which, Wolfram Alpha tells me, is roughly the number of grains of sand upon the earth. Which is very poetic.
What all this tells me is three things: 1.) the book looks gorgeous and if you can budget for it, you should buy a copy (since it’s all hand-tipped, it’s a little more expensive than they’d planned for it to be, but the proceeds do go to Japan); 2.) I think my dad enjoyed talking about math with me, which is something we have not talked about since I was 17, and 3.) mathematics is very difficult and now it’s time for a scotch.
Of course, I welcome your double-checking, Internet mathematics degree holders. If this number looks off to you, please contact me through the regular channels.](http://24.media.tumblr.com/tumblr_li8cxnZvsd1qzr7dwo1_1280.jpg)
How about a word problem for your Thursday evening? A classic high school mathematics word problem.
My friend Brad called me last night while I was engrossed in reading Wallace and Wallechinsky’s 1980 hippie prophecy collection The Book of Predictions — he’s one of the few people I know that will still leave a funny voicemail message, if he gets your voicemail, instead of hanging up and texting you — to get some help with this problem he was having. I don’t know why he thought I’d be good at helping him with a math problem. But I was sort of touched he thought of me. It means he thinks I am a well-rounded person. Maybe. But not with math.
The problem was this: he has a book being published by the Little Brown Mushroom imprint this month. It’s called Conductors of the Moving World, and it sounds amazing. A description:
In the autumn of 1972, a delegation of Japanese police officials visited the United States to study traffic control in several large cities, including New York, Las Vegas, and Los Angeles. The unofficial photographer for the delegation was Eizo Ota, an inspector with the law enforcement department of the Yamanashi Prefecture, and he produced a record of the group’s travels that might best be described as forensic tourism.
Using Inspector Ota’s snapshots as launching points, Brad Zellar plundered traffic manuals, haiku anthologies, the Watergate transcripts, and The Godfather for textual inspiration. The mysterious result is a Zen travelogue through 1972 America.
Now, here’s the problem. There were 51 possible photographs from Ota’s collection, 500 prints of each photograph. These 51 photos were arranged in 17 sets of 3 related images: so that’s one set of three different shots of, say, the Statue of Liberty. Same subject, three different shots. The photos are all hand-printed, and hand-tipped into each of the 500 books, and each book will get 17 of the photographs. There’s no order — the photos will be randomly placed in each book, in no particular sequence. The only rule is photos from the same 3-photo set cannot be used in the same book.
So, the problem:
How many possible iterations of the book are there, if each book has 17 photographs, with each of these photographs being 1 of 3 possibilities from 17 different groups, from the possible pool of 51, arranged in any sequence?
It took me and Brad a half-hour to even describe it to each other in that language. That still sounds clunky. So I told Brad I’d do what I’d have done in high school: talk to my dad.
Dad holds a degree in engineering from the University of Cincinnati (BEng, ‘76). Mathematics is an area in which he excels. After talking him through it, using very clunky language, and being reminded what factorials are (this one: “!”), we figured that the equation looks like this:
3^17 [that is, the number of possible combinations of the photos] * 17! [the number of possible ways in which the photos could be sequenced]
And the answer:
4.59335324 × 10^22
Or:
45,933,532,441,368,219,648,000
Or:
45 sextillion, 933 quintillion, 532 quadrillion, 441 trillion, 368 billion, 219 million, 648 thousand
Now of course, realistically, there’s only 500 different books. But there are over 45 sextillion possible configurations of this book, which, Wolfram Alpha tells me, is roughly the number of grains of sand upon the earth. Which is very poetic.
What all this tells me is three things: 1.) the book looks gorgeous and if you can budget for it, you should buy a copy (since it’s all hand-tipped, it’s a little more expensive than they’d planned for it to be, but the proceeds do go to Japan); 2.) I think my dad enjoyed talking about math with me, which is something we have not talked about since I was 17, and 3.) mathematics is very difficult and now it’s time for a scotch.
Of course, I welcome your double-checking, Internet mathematics degree holders. If this number looks off to you, please contact me through the regular channels.
