Puzzling Week Returns: Coxeter's Pippin

Peeled & equatorially cut apples ready to be cored for making apple slab.
January 24, 2011

John and I peel dozens of apples for pie, sauce, and slab. Depending on the size and quality of the apples, we will either peel and core by hand (with or without a corer) or by crank. John recently taught me that cutting apples equatorially and then coring them takes less time then the traditional cutting and coring. I have often wondered if there was an even easier or better way than all of the methods we have tried. I found a way tonight! But this is a puzzle. Your clue is the photo I took (above) of equatorially cut apples from January when I made two huge slabs for the weekend. By the way, I no longer use the King Arthur slab recipe. I double a pie crust recipe for a double 9” pie, use a 13x9 Pyrex pan, and just make an apple pie (butter, flour, brown sugar, cinnamon, nutmeg, ginger, cloves are all measured by feel and sight) in the rectangular Pyrex.

New Scientist Magazine December 21, 1961

There are many ways of eating an apple. At one extreme is the child who met the request, "Can I have the core of your apple?" with a flat, "There ain't going to be no core!". Various procedures with various implements are designed to remove the core, but probably not one apple in a million is cored in the most efficient fashion possible. How in fact should an apple be cored, to remove all the core with the least possible waste?

Spoiler Alert! The answer is the first comment to this post.

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Puzzling Week: Getting to 100

From Car Talk Puzzler

RAY: This is mathematical in nature. I want you to get a pencil and write down the numbers, 1 to 9, inclusive, and leave enough space between them. At your disposal you have one plus sign and two minus signs. You can insert those plus and minus signs wherever you want, to make the total come out to 100. In other words, if you were to put an equal sign after the 9, you want to be able to write 100 after it.

Now I'll give you an example, you could do 12 + 345 - 67 - 89. It doesn't work, but you get the idea. You can't change the order. You can't monkey with the plus or minus signs.

You've got one plus sign and two minus signs, you can put them any place you want, and the total has to equal 100. What's the equation?

What strategies did you use to solve this?

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Puzzling Week: Number Riddles

1. Grab a calculator. (You won't be able to do this one in your head.)
2. Key in the first three digits of your phone number (NOT the area code).
3. Multiply by 80
4. Add 1
5. Multiply by 250
6. Add the last 4 digits of your phone number
7. Add the last 4 digits of your phone number again.
8. Subtract 250
9. Divide number by 2

Does the answer look familiar?
Algebraically, why does this work?
Make up your own number riddle and explain algebraically why it works.

My thanks to lynnemead07!

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Puzzling Week: Left and Right Queues

It has always been speculated that the left queue of most attractions at Walt Disney World tend to progress faster than the right queue. On the new Rock’N’Roll Coaster, cast members allow 50 guests into the left and 10 guests into the right queue immediately at park opening. Every minute after that 10 guests are added to the left queue and 12 guests are added to the right queue.

How long will it take to move the same number of guests to move through both queues?

How many guests will go through the left and right queues after one hour? How many guests will go through the left and right queues after a twelve-hour day?

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Puzzling Week: The Tortoise and the Hare

The time has come to clear the hare’s bad name as a lazy show-off whose arrogance leads to spoiled opportunities. In fact, it is the conduct of the tortoise that deserves our scrutiny, for this leather-skinned reptile is nothing but a cheat! Recently uncovered information proves that the tortoise’s celebrated come-from-behind victory over the speedier hare was a resul tof shrewd deceit, not praiseworthy persistence.

Years after the famous footrace, the hare challenged the tortoise to a rematch on roller blades. The hare was able to skate at a rate of 15 miles per hour (mph) while the tortoise could skate at the rate of only 12 mph. Knowing he was slower, the tortoise made up a lame excuse for being given a 27-mile head start in the 165 mile race. These are the basic facts of the story.

Who won the race? Was the head-start fair? Explain your reasoning.

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Puzzling Week: Speeding Tickets

In Massachusetts the fine for speeding is a flat fee of $100 plus $5 for each mile per hour above the 55mph speed limit. In Vermont the fine for speeding is a flat fee of $50 and $10 for each mile per hour above the 65mph speed limit.

If you were stopped for speeding right on the border between Massachusetts and Vermont, and stopped by both a Vermont and a Massachusetts trooper, which state would you like to be fined by?

Explain your reasoning.

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Puzzling Week: Petals Around the Rose

Polar bears, they come in pairs.
They sit around the hole in the ice
like petals around a flower.

How many polar bears do you see? 10
How many fish do you see? 8
How many plankton do you see? 74

How many polar bears do you see? 6
How many fish do you see? 6
How many plankton do you see? 93

So have you figured out how it's figured out?

NCTM's Illumination site has a wonderful lesson for this puzzle.

Nope! No spoiler here!
Tradition requires me to never post the solution.
After you figure out the answers, can you derive any equations to solve this puzzle for any combination of dice tossed?

When you solve the puzzle, you deserve membership in the Polar Bear Club!

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Puzzling: Entomology Problems

Title: Entomology - The Problems
Date: 01/01/07

The Problems

Entomology is the scientific study of insects. Jung, Tara and Pavan collected some insects for their science project. At the end of the first week of collecting Jung and Tara together had 26 insects, Tara and Pavan together had 18 insects, and Pavan and Jung together had 22 insects. How many insects did each person have alone?

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The number of insects they had in their collection continuously changed throughout the second week as they worked to improve the quality and variety of the insects in their collection. They took some insects out and added other new insects. The difference between the maximum and minimum number of insects they had in their collection during the second week of collecting was 38. The mean of the maximum and minimum number of insects in the collection during the second week of collecting was 46. What was the maximum and minimum number of insects in the collection during the second week of collecting?

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At the end of the third week of collecting they divided their collection of insects into 3 categories: winged, more than one color, and length less than one-half inch.

2 insects were winged, more than one color, and less than one-half inch long

7 insects (of various lengths) were winged and more than one color

6 insects (winged and non-winged) were more than one color and less than one-half inch long

5 insects (of single and multi-colorings) were winged and less than one-half inch long

12 insects were less than one-half inch long, non-winged, and only brown

9 insects were winged, more than one-half inch long, and only brown

14 insects were more than one color, more than one-half inch long, and non-winged

5 insects did not have any of the sorted characteristics

How many insects were in their collection at the end of the third week of collecting?

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