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# Treebeard's Stumper Answer7 Mar 97

Fill in the blanks with numerals ("1", "2", etc.) to make this sentence true of itself:

```          This sentence contains ___0's, ___1's,
___2's, ___3's, ___4's, ___5's, ___6's,
___7's, ___8's, and ___9's.
```

At first there's just one of each digit, but filling all the blanks with "1" adds a bunch more 1's which changes everything. There's at least two solutions.

*Bonus*
What year was Washington born in? And will the year 2000 be a leap year? (See last week's stumper.)

I've found two ways to make this sentence true of itself.
• This sentence contains 1-0, 11-1's, 2-2's, 1-3, 1-4, 1-5, 1-6, 1-7, 1-8, and 1-9.

• This sentence contains 1-0, 7-1's, 3-2's, 2-3's, 1-4, 1-5, 1-6, 2-7's, 1-8, and 1-9.

There is a method for this. Fill in the blanks with any numbers. Then count the digits and fill in the blanks again. And again. Usually an answer will emerge. Such iterative methods are important for computers programming!

And yes, the year 2000 will be a leap year, but 1900 wasn't. To eliminate extra years, the rule is that centuries are leap years only if divisible by 400.

Kids, if you don't know what tour de force means, look it up! Here's an example from A. K. Dewdney:

Only the fool would take trouble to verify that his sentence was composed of ten a's, three b's, four c's, four d's, forty-six e's, sixteen f's, four g's, thirteen h's, fifteen i's, two k's, nine l's, four m's, twenty-five n's, twenty-four o's, five p's, sixteen r's, forty-one s's, thirty-seven t's, ten u's, eight v's, eight w's, four x's, eleven y's, twenty-seven commas, twenty-three apostrophes, seven hyphens, and last but not least, a single !

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