The Three-Hat Problem

In the October 2003 issue of MIT Technology Review, Donald Aucamp offered this conundrum:

Three logicians, A, B, and C, are wearing hats. Each hat displays a positive integer, and each logician can see his companions’ numbers but not his own. All of them know that the numbers are positive integers and that one of the numbers is the sum of the other two. The three then take turns in a contest to see who can determine his number first. In the first round, all three pass, but in the second round A correctly states his number is 50. What are the other two numbers, and how did A know that his was 50?

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An old “puzzler” from NPR’s Car Talk:

Thirty buyers attended an auction of dozens of cars. Ten of the buyers bought fewer than 6 cars; eight bought more than 7 cars; five bought more than 8 cars; and one bought more than 9 cars.

Of the 30 buyers, how many bought 6, 7, 8, or 9 cars?

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Running Cargo

This passage is from Rudyard Kipling’s 1910 story “Brother Square-Toes.” What’s notable about the bolded section?

‘I’ll have to bide ashore and grow cabbages for a while, after I’ve run this cargo; but I do wish’ — Dad says, going over the lugger’s side with our New Year presents under his arm and young L’Estrange holding up the lantern — ‘I just do wish that those folk which made war so easy had to run one cargo a month all this winter. It ‘ud show ’em what honest work means.’

‘Well, I’ve warned ye,’ says Uncle Aurette. ‘I’ll be slipping off now before your Revenue cutter comes. Give my love to sister and take care o’ the kegs. It’s thicking to southward.’

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Hope and Change

Just stumbled across this in an 1889 newspaper:

To those who love mathematics, here is a simple problem for you to figure out: A man purchased groceries to the amount of 34 cents. When he came to pay for the goods he found that he had only a $1 bill, a 3-cent piece and a 2-cent piece. The grocer, on his side, had only a 50-cent piece and a quarter. They appealed to a bystander for change, but he, although willing to oblige them, had only two dimes, a 5-cent piece, a 2-cent piece and a 1-cent piece. After some perplexity, however, change was made to the satisfaction of everyone concerned. What was the simplest way of accomplishing this?

($1 is worth 100 cents, a quarter 25 cents, and a dime 10 cents.)

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I think Jacques Jouet was the first to notice this. In the first few pages of the Tintin adventure The Secret of the Unicorn, as Tintin visits the Vossenplein antique market in Brussels, Snowy the dog keeps scratching himself. Why?

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