The Doodle Problem Is a Lot Harder Than It Looks. Can You Solve It?

Laura Feiveson
Photo credit: Andrew Daniels

From Popular Mechanics

The Doodle Problem Is a Lot Harder Than It Looks. Can You Solve It?

(Difficulty: Moderate)

This week’s riddle is relatively simple—but sinister all the same.

The question: Can you make 100 by interspersing any number of pluses and minuses within the string of digits 9 8 7 6 5 4 3 2 1? You can’t change the order of the digits! So what’s the least number of pluses and minuses needed to make 100?


Photo credit: Andrew Daniels

For instance, 98 - 7 - 6 + 54 - 32 shows one way of interspersing pluses and minuses, but since it equals 107, it’s not a solution.

I call this a “doodle problem”: one that’s best worked on during meetings where you might be doodling otherwise.

Hint

You might want to start looking for solutions that use a total of seven pluses and minuses (although there are ways to use fewer).

Solution

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This Math Puzzle Stumped Every Scientist but One. Think You Can Crack It?

(Difficulty: HARD)

In honor of Freeman Dyson, the renowned physicist who died last month, here’s a legendary tale demonstrating his quick wit and incredible brain power.

One day, in a gathering of top scientists, one of them wondered out loud whether there exists an integer that you could exactly double by moving its last digit to its front. For instance, 265 would satisfy this if 526 were its exact double—which it isn’t.

After apparently just five seconds, Dyson responded, “Of course there is, but the smallest such number has 18 digits.”

This left some of the smartest scientists in the world puzzling over how he could have figured this out so quickly.

So given Dyson’s hint, what is the smallest such number?

Hint

My second grader has recently learned how to add a 3-digit number to itself using the classic vertical method:

Photo credit: Andrew Daniels

18-digit numbers, of course, can be added in the same way.

Solution

Ready for the solution? Click here to see if you’re right.

Figure Out What’s on Her Forehead

(Difficulty: Moderate)

Cecilia loves testing the logic of her very logical friends Jaya, Julian, and Levi, so she announces:

“I’ll write a positive number on each of your foreheads. None of the numbers are the same, and two of the numbers add up to the third.”

She scribbles the numbers on their heads, then turns to Jaya and asks her what her number is. Jaya sees Julian has 20 on his forehead, and Levi has 30 on his. She thinks for a moment and then says, “I don’t know what my number is.” Julian pipes in, “I also don’t know my number,” and then Levi exclaims, “Me neither!” Cecilia gleefully says, “I’ve finally stumped you guys!”

“Not so fast!” Jaya says. “Now I know my number!”

What is Jaya’s number?

Hint

Jaya could be one of two numbers, but only one of those numbers would lead to Julian and Levi both not knowing their numbers. Why?

Solution

Ready for the solution? Click here to see if you’re right.

Can You Get Keanu Reeves Elected As President?

(Difficulty: Moderate)

It’s 2024, and there are five candidates running in the democratic primary: Taylor Swift, Oprah Winfrey, Mark Cuban, Keanu Reeves, and Dwayne Johnson. (Hey, it could happen.) As usual, the first primary is in Iowa.

In an effort to overcome its embarrassment after the 2020 caucus debacle, the Iowa Democratic Party has just announced a new, foolproof way of finding the best candidate: there will be four consecutive elections.

First, candidate 1 will run against candidate 2. Next, the winner of that will run against candidate 3, then that winner will run against candidate 4, and finally the winner of that election will run against the final candidate. By the transitive property, the winner of this last election must be the best candidate ... so says the Iowa Democratic Party.

Candidate Keanu has been feeling pretty low, as he knows he is ranked near the bottom by most voters, and at the top by none. In fact, he knows the Iowa population is divided into five equal groups, and that their preferences are as follows:

Photo credit: .

Keanu is childhood friends with Bill S. Preston, Esq., the new head of the Iowa Democratic Party. Preston, confident that the order of the candidates doesn’t matter for the outcome, tells Keanu he can choose the voting order of the candidates.

So what order should Keanu choose?

Hint

How would Keanu fare in one-to-one races against each candidate?

Solution

Ready for the solution? Click here to see if you’re right.

Who Opened All These Damn Lockers?

(Difficulty: Moderate)

There are 100 lockers that line the main hallway of Chelm High School. Every night, the school principal makes sure all the lockers are closed so that there will be an orderly start to the next day. One day, 100 mischievous students decide that they will play a prank.

The students all meet before school starts and line up. The first student then walks down the hallway, and opens every locker. The next student follows by closing every other locker (starting at the second locker). Student 3 then goes to every third locker (starting with the third) and opens it if it’s closed, and closes it if it’s open. Student 4 follows by opening every fourth locker if it’s closed and closing it if it’s open. This goes on and on until Student 100 finally goes to the hundredth locker. When the principal arrives later in the morning, which lockers does she find open?

Hint

Make sure you pay attention to all of the factors.

Solution

Ready for the solution? Click here to see if you’re right.

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