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?

# MathArguments180.com

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

## Wednesday, August 27, 2014

## 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

## Monday, August 25, 2014

### 228: Four Intersections

Find two polynomials whose four points of intersection form a perfect square. (...with integer coefficients?)

What's the best way to do that?

.

What's the best way to do that?

```
Find two polynomials whose four points of intersection form a perfect square.
(...with integer coefficients?)
```

— James Tanton (@jamestanton) July 5, 2014

```
@jamestanton 13*x^3/15+13*x^2/10-137*x/30 & x^4+43*x^3/15-37*x^2/10-317*x/30 go through square with vertices (0,0), (2,3), (-1,5), (-3,2)
```

— Republic of Math (@republicofmath) July 5, 2014

. .

## Saturday, August 23, 2014

### 227: Are these the Same?

Are these the same or not the same? Why? (What makes them different if you think they're different?)

source.

source.

## Friday, August 22, 2014

### 225: Penny circle

Here's a screen grab of one of @ddmeyer's videos: Penny Circle.

If this were a 0.75" circle, the penny would fit perfectly. If it's 1" then there would be a lot of wasted space. What sizes of circle would be best for packing in 0.75" pennies with as little wasted space as possible?

If this were a 0.75" circle, the penny would fit perfectly. If it's 1" then there would be a lot of wasted space. What sizes of circle would be best for packing in 0.75" pennies with as little wasted space as possible?

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