# MathArguments180.com

180 Days of Ideas for Discussion in Math Class. (as of 9July2014, we're in overtime!)

## Sunday, August 31, 2014

### 235: Counterfeit Bill

The Counterfeit Bill problem (Sobel and Maletsky 1999).

*A customer enters a store and purchases a pair of slippers for $5, paying for the purchase with a $20 bill. The merchant, unable to make change, asks the grocer next door to change the bill. The merchant then gives the customer the slippers and $15 change.**After the customer leaves, the grocer discovers that the $20 bill is counterfeit and demands that the shoe-store owner make good for it. The shoe-store owner does so, and by law is obligated to turn the counterfeit bill over to the FBI.**How much does the shoe-store owner lose in this transaction?*## Saturday, August 30, 2014

### 234: Fraction Manipulation

I know how I would solve this problem, but not everyone is comfortable with algebra. Which ways can you come up with? Which seems the best to you?

There is a number such that, when it is subtracted from the numerator of the fraction $\dfrac{5323}{7577}$ and added to the denominator, the fraction reduces to $\dfrac{17}{83}$. Determine the number.

There is a number such that, when it is subtracted from the numerator of the fraction $\dfrac{5323}{7577}$ and added to the denominator, the fraction reduces to $\dfrac{17}{83}$. Determine the number.

## Friday, August 29, 2014

### 233: Vegetable Zen

100 students were surveyed about their preferences for bell peppers (capsicum), carrots and spinach, with the following results:

① 72 students said they like bell peppers, and 36 students said they like only bell peppers.

② 41 students said they like carrots, and 9 students said they like only carrots.

③ 31 students said they like spinach, and 3 students said they like only spinach.

④ 9 students said they like neither bell peppers, nor carrots, nor spinach.

What is the best way to model/analyze this survey data?

Graphically (and what type of graph)?

Tables? How?

Algebra?

source.

## Thursday, August 28, 2014

## Wednesday, August 27, 2014

### 231: Friedman Numbers

How do you suppose we could go about finding these?

Any methods or algorithms that we might use?

Source.

Challenge: How would we determine whether this is an infinite set or a finite one?

Any methods or algorithms that we might use?

Source.

Challenge: How would we determine whether this is an infinite set or a finite one?

## Tuesday, August 26, 2014

### 229: Create a special 10-digit number

Can you create a 10-digit number, where the first digit is how many
zeros in the number, the second digit is how many 1s in the number etc.
until the tenth digit which is how many 9s in the number?

Some hints:

Can it be 0000000000?

Can it be 9000000000?

Source: Richard Wiseman.

One answer, slightly obfuscated, is 2³ * 5³ * 7 * 887143

Some hints:

Can it be 0000000000?

Can it be 9000000000?

Source: Richard Wiseman.

One answer, slightly obfuscated, is 2³ * 5³ * 7 * 887143

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