Puzzle: Random Blocks

Posted on by Denise Gaskins
colorful wooden blocks

In the first section of George Lenchner’s Creative Problem Solving in School Mathematics, Lechner poses this problem. If you have seen it before, be patient — his point was much more than simply counting blocks.

A wooden cube that measures 3 cm along each edge is painted red. The painted cube is then cut into 1-cm cubes as shown below. How many of the 1-cm cubes do not have red paint on any face?

red cude cut into smaller blocks

Create Your Own Math

And then he challenges us as teachers:

  • Do you have any ideas for extending the problem?
  • If so, then jot them down.

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Pi and Buffon’s Matches

Posted on by Denise Gaskins

From Numberphile: Dr Tony Padilla’s unique (and low budget) twist on the Buffon’s Needle experiment to learn the true value of Pi.

For a kid-friendly version of this experiment, try throwing food:

Do you have a favorite family activity for celebrating Pi Day? I’d love to hear it!

A Football Puzzle

Posted on by Denise Gaskins

[Photo by rdesai.]

The MIT Mathmen got the ball on their own 20-yard line for the last drive of the game. They were down by 2 points, so they needed at least a field goal to win the game.

If quarterback Zeno and his offense advanced the ball halfway to the opposing team’s end zone on each play…

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How to Start an Argument: The Monty Hall Problem

Posted on by Denise Gaskins


[Photo by MontyPython.]

You can get a good argument going in almost any group of people with the infamous Monty Hall problem:

Imagine you are on a TV game show, and the host lets you choose between three closed doors. One of the doors hides a fancy sports car, and if you pick that door, you win the car.

You pick door #1.

The host opens door #3 to reveal a goat. Then he gives you a chance to switch your door for the unopened door #2.

Should you switch?

What if you say you’re going to switch, and then the host offers to give you $5,000 instead of whatever is behind door #2?

Try the game for yourself at the Stay or Switch website.

Continue reading How to Start an Argument: The Monty Hall Problem

Math History Tidbits: The Battling Bernoullis

Posted on by Denise Gaskins

July 27th is Alex’s birthday. She shares it with Johann Bernoulli, an irascible mathematician from the late 17th century. This coincidence intrigued her enough that she wrote a research paper on Johann and his mathematical brother, titled “Jeering Jacob and Jealous Johann.”

Of course, to make the alliteration work, she had to mispronounce Johann’s name — but she figured he kinda deserved that. Read the historical tidbits below to find out why one writer said the Bernoulli brothers were “the kind of people who give arrogance a bad name.”*

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Probability Issue: Hints and Answers

Posted on by Denise Gaskins

Remember the Math Adventurer’s Rule: Figure it out for yourself! Whenever I give a problem in an Alexandria Jones story, I will try to post the answer soon afterward. But don’t peek! If I tell you the answer, you miss out on the fun of solving the puzzle. So if you haven’t worked these problems yet, go back to the original posts. If you’re stuck, read the hints. Then go back and try again. Figure them out for yourself — and then check the answers just to prove that you got them right.

This post offers hints and answers to puzzles from these blog posts:

Continue reading Probability Issue: Hints and Answers

Probability and Baby Blues

Posted on by Denise Gaskins


[Photo by audi_insperation.]

[In The Birthday Surprise, Alex discovered her family was expecting a new member…]

What will the baby look like, Alex wondered. “Dad, is there any way to tell whether the baby will have blue eyes like I do, or brown like the rest of the family?”

Dr. Jones shuffled the papers on his desk and found a blank page. “Over 100 years ago, the Austrian monk Gregor Mendel studied genetics, or how various traits are passed down from one generation to another.” He began to draw a diagram as he talked.

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Alexandria Jones and the Birthday Surprise

Posted on by Denise Gaskins

[Photo by D Sharon Pruitt.]

[July 27th is Alex’s birthday, which she shares with Johann Bernoulli, an irascible mathematician from the late 17th century.]

The guests had gone. Alex and her family sat around the table, sharing the last tidbits of birthday cake and ice cream. Alex smiled at her parents.

“Thanks, Mom and Dad,” she said. “It was a great party.”

Maria Jones, Alex’s mother, leaned back in her chair. “I do have one more surprise for you, Alex. But you will have to share this one with the whole family.”

Leon groaned. “I know what it is: Let’s all pitch in to clean up.”

“That wouldn’t be a surprise,” Alex said.

Continue reading Alexandria Jones and the Birthday Surprise