PuzzleLog

Bat and Ball

A bat costs $1 more than a ball; together they cost $1.10. How much does the bat cost?

Algebra Too

No Twins Today

It was the first day of class and Mrs. O’Connor had two identical-looking pupils, Donald and Ronald Featheringstonehaugh (pronounced “Fanshaw”), sitting together in the first row. “You two are twins, I take it?” she asked. “No,” they replied in unison. But a check of their records showed that they h…

Working for the System

Portrait

A visitor points to a portrait on the wall and asks who it is. “Brothers and sisters have I none,” says the host, “but that man’s father is my father’s son.” Who is pictured?

Back from the Future

Half Grown

At what age is the average child half the height that he or she will be as an adult?

Out for the Count

Shoes, Socks, and Gloves

You need to pack for a midnight flight to Iceland but the power is out. In your closet are six pairs of shoes, six black socks, six gray socks, six pairs of brown gloves, and six pairs of tan gloves. Unfortunately, it’s too dark to match shoes or to see any colors. How many of each of these items do…

The Pigeonhole Principle

Phone Call

A phone call in the continental United States is made from a west coast state to an east coast state, and it’s the same time of day at both ends of the call. How is this possible?

Hammer and Tongs

Powers of Two

How many people are “two pairs of twins twice”?

Out for the Count

Rotating Coin

While you hold a U.S. 25-cent piece firmly to the tabletop with your left thumb, you rotate a second quarter with your right forefinger all the way around the first quarter. Since quarters are ridged, they will interlock like gears and the second will rotate as it moves around the first. How many ti…

Let's Get Physical

Boxing the Mountain State

Can West Virginia be inscribed in a square?

Intermediate Math

Martians in a Circle

A visiting logician is surrounded by a circle of Martians, each of whom either always tells the truth or always lies. She asks each Martian whether the Martian to his right is a truth teller or a liar, and from their answers, she is able to deduce the fraction of liars in the circle. What fraction i…

Working for the System

Winning at Wimbledon

As a result of temporary magical powers (which might need to be able to change your gender), you have made it to the women’s singles tennis finals at Wimbledon and are playing Serena Williams for all the marbles. However, your powers cannot last the whole match. What score do you want it to be when…

Polyhedron Faces

Prove that any convex polyhedron has two faces with the same number of edges.

The Pigeonhole Principle

Finding the Counterfeit

You have a balance scale and 12 coins, 11 of which are genuine and identical in weight; but one is counterfeit, and is either lighter or heavier than the others. Can you determine, in three weighings with a balance scale, which coin is counterfeit and whether it is heavy or light?

Information, Please

Expert

Signs in an Array

Suppose that you are given an m×n array of real numbers and permitted, at any time, to flip the signs of all the numbers in any row or column. Can you always arrange matters so that all the row sums and column sums are nonnegative?

Unlimited Potentials

Birthday Match

You are on a cruise where you don’t know anyone else. The ship announces a contest, the upshot of which is that if you can find someone who has the same birthday as yours, you (both) win a beef Wellington dinner. How many people do you have to compare birthdays with in order to have a better than 50…

Meeting the Ferry

Every day at noon GMT a ferry leaves New York and simultaneously another leaves Le Havre. Each trip takes seven days and seven nights, arriving before noon on the eighth day. How many of these cross-Atlantic ferries does one of them pass on its way across the pond?

Seeing Is Believing

Sinking 15

Carol and Desmond are playing pool with billiard balls number 1 through 9. They take turns sinking balls into pockets. The first to sink three numbers that sum to 15 wins. Does Carol (the first to play) have a winning strategy?

Startling Transformation

Monk on a Mountain

A monk begins an ascent of Mt. Fuji on Monday morning, reaching the summit by nightfall. He spends the night at the summit and starts down the mountain on the same path the following morning, reaching the bottom by dusk on Tuesday. Prove that at some precise time of day, the monk was at exactly the…

Intermediate Math

Mathematical Bookworm

The three volumes of Jacobson’s Lectures in Abstract Algebra sit in order on your shelf. Each has 2′′ of pages and a front and back cover each ¹ ′′, thus a total width of 2 ¹ ′′. A tiny bookworm bores its way straight through from page 1, Vol I to the last page of Vol III. How far does it travel?

Seeing Is Believing

Other Side of the Coin

A two-headed coin, a two-tailed coin, and an ordinary coin are placed in a bag. One of the coins is drawn at random and flipped; it comes up “heads.” What is the probability that there is a head on the other side of this coin?

Slicing the Cube

Before you is a circular saw and a 3×3×3 wooden cube that you must cut into 27 1 × 1 × 1 cubelets. What’s the smallest number of slices you must make in order to do this? You are allowed to stack pieces prior to running them through the saw.

Startling Transformation

Rolling Pencil

A pencil whose cross-section is a regular pentagon has the maker’s logo imprinted on one of its five faces. If the pencil is rolled on the table, what is the probability that it stops with the logo facing up?

Seeing Is Believing

Watermelons

Yesterday a thousand pounds of watermelons lay in the watermelon patch. They were 99% water, but overnight they lost moisture to evaporation and now they are only 98% water. How much do they weigh now?

Out for the Count

Expert

Boy Born on Tuesday

Mrs. Chance has two children of different ages. At least one of them is a boy born on a Tuesday. What is the probability that both of them are boys?