Buying House Numbers, in Letters

Oct 27, 2018

RAY: Another puzzler about house numbers! A man is waiting in line at a hardware store to buy letters that make up the number of his house. You know. For example T, H, R, E, E.

 But, by luck, there were three other guys ahead of him in line all doing the same thing. The first customer buys the number one. O, N, E. He pays two bucks. The next guy buys the number TWO, and pays three bucks. The third guy buys the number ELEVEN, and he pays five bucks.

Our protagonist is buying the number twelve. Here's my question: How much does he pay?


RAY: Let's look at the word "twelve". Let's look at it. All the letters in 12 are in the first three numbers purchased.

And then let's look at the word 11. "Eleven" and "twelve" share four letters.

So if you take that away from the 12, you get T-W left over. And If you take those same four letters away from 11, you have N-E left over.

Now, let's go back to the first two guys. "One" cost two dollars, and "two" cost three dollars. What have we learned? Now we don't know the cost of any of the letters individually.

But we do know that a T and a W costs a dollar more than an N and an E.

And as luck would have it, the T and W in 12 are going to cost a dollar more than the N and the E in 11. We know the whole of 11 costs five bucks, so 12 must cost six bucks. Pretty good. Huh?


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