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Dr. Shapiro's Puzzle of the Day

Today's Puzzle

Wednesday, May 5
This piece of music was written in 1902. What is it best known for today?

Hint
Stop teasing and give me a real hint Listen at 0:12.

   


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Yesterday's Puzzle + Solution

Tax code may be complicated, but there is usually an underlying logic to it.

Can you deduce the exact number I have blacked out in this table from an IRS publication?
(Feel free to use a calculator.)

Solution The multipliers in column (b) are the tax rates on different income brackets; a more complete table is shown at right. For example, a single person making $200,000 is in the 32% bracket. But they do not pay 32% tax on all their income! Instead, they pay 10% on the first $9,875, then 12% of each additional dollar until they hit $40,125, then 22%… and so on. If you ever hear someone say "I can't afford to get a raise because it will move me into a higher tax bracket and I'll end up losing money," they are misinformed.

Now, the result is that someone earning $x, where 163300 ≤ x ≤ 207350, will owe

dollars tax, which looks awfully complicated. But this can be simplified down to , where c is a single number—the "subtraction amount" in column (d).

That's all nice and good, but I didn't give you the full table of tax brackets… so how could you determine c? Well, this is a case where the less you know, the easier the problem is. All you need to know (or guess) is that total tax owed is a continuous function of income: it doesn't make any sudden jumps when you cross tax brackets. Thus, the tax on $163,300 should be the same whether you figure it out using the first or second line of the worksheet.

tl;dr: .

Well, this was my least popular puzzle ever (lol). Congratulations to Mr. Gregg for solving it, and to everyone else for doing something more fun than thinking about taxes. 😊

About This Site

Though he now teaches mathematics, Dr. (né Mr.) Shapiro's first job in a K–12 school was as a lunch monitor in Davis, CA. It was there that he originated the Puzzle of the Day, even rewarding correct answers with tickets in denominations like "15 points" (though without a clear idea of how he'd ultimately redeem these). Dr. Shapiro's favorite puzzle from this pre-professional era was "Tell me the location of the beehive on this campus."

Ten years later, Dr. Shapiro revived Puzzle of the Day at Proof School, writing each day's puzzle on a name tag. After 600 puzzles or so, he was just starting to feel normal about students reading his chest all the time when campus closed and the puzzle, like the rest of our lives, moved online. New puzzles are posted daily on school days.

Want to catch up on old PotDs? There's an archive currently containing puzzles from March 2020 to March 2021.