Popular Mechanics - USA (2020-05)

// ALEXANDER GEORGE //

The Pop

Mech

Riddle

That

Defeated

Me

I

ONLY MADE IT ABOUT HALFWAY

through this riddle (right), the

first installment from contributor

Laura Feiveson. There’s a reason

hers are so challenging. She has a

Ph.D. in Economics from MIT. She

worked at the IMF. And now, on

days off from her job as an economist

at the Federal Reserve, she creates

math puzzles for Pop Mech. For the

full explanation of the solution, go to

popularmechanics.com/riddle.

Trying to solve these kinds of

puzzles brings back good memories

of computer science and geometry

classes. I liked using specific tools

and principles to reason toward the

answer, all while building a trail

of evidence.

Getting beat by a “moderate” rid-

dle reminds me: Respect the heroes

who use math and logic to solve huge

problems. That includes economists

like Feiveson, and the epidemiol-

ogists and doctors who have been

asked to find new answers on very

short notice. Me? I’ll try one more,

then back to my Nintendo Switch.

The Locker Prank

DIFFICULTY Moderate by Laura Feiveson

Every locker will have its status changed // : 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 ER ANSW

by a student with a number that is a factor of that locker number. (Locker 24 will be

opened/closed by students 1, 2, 3, 4, 6, 8, 12, and 24.) Lockers with an odd number of

factors will ultimately remain open, and lockers with factors that are a pair (16, with 4

and 4, for example) are the only ones with an odd number of factors. Those lockers are

also perfect squares. Only locker numbers that are perfect squares are left open.

There are 100 lockers that line

the main hallway of Chelm High

School. Every night, the school

principal makes sure all the lock-

ers 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. Stu-

dent 4 follows by opening every

fourth locker if it’s closed and

closing it if it’s open. This contin-

ues until Student 100 finally goes

to the hundredth locker. When

the principal arrives later in the

morning, which lockers does she

find open?

From the

(^2) Editor
LA
KO
TA
GA
MB
ILL
8 May/June 2020