12 of 30 Items .... Type: Open Middle

. . . View This Fullsize

How many different solutions can we find?

. . . View This Fullsize

3

Challenges

1. Use four different digits (from 2-9) to create two points which determine a line with the greatest possible slope.


2. Use four different digits (from 2-9) to create two points which determine a line with the least possible slope.


3. Use four different digits (from 2-9) to create two points which determine a line with a slope as close to zero as possible.

. . . View This Fullsize

There's a neat game you can play with the English language: Place the word "only" anywhere in the sentence. How does it change the meaning?

Only she told him that she loved him.
She only told him that she loved him.
She told only him that she loved him.
She told him only that she loved him.
She told him that only she loved him.
She told him that she only loved him.
She told him that she loved only him.
She told him that she loved him only.

What would it look like if we were trying to create a math problem that worked the same way, except "only" is replaced by the equals sign?

. . . View This Fullsize

This problem, from Robert Kaplinsky, asks for you to fill in the spaces.




Being the ornery sort, I wondered if there were other coefficients that we could choose for the cubic that might give multiple sets of answers?

. . . View This Fullsize

Following on from yesterday's question, we have a puzzle from the same source.

Which of those central tendency statistics are necessary in order to find the missing numbers? (Necessary meaning that you can't find a particular number without it.)

In other words, do we really need all five statistics?

. . . View This Fullsize

Here is a list of numbers.



You create a new problem this time ... what hints will you give?
What values of mean, median, mode, range, quartiles?

Can you create a solvable problem with just two hints?

Or do we need three?

. . . View This Fullsize

Here is a list of numbers.



You create the problem ... what hints will you give?
What values of mean, median, mode, range, quartiles?

What are some different statistics that you could give to a classmate (other than the ones below) yet still keep this a solvable problem, with the same answers as the original problem?

Original problem:

mean = 76;
range = 32; IQR = 21

. . . View This Fullsize

Here is a list of numbers.


What information would you NEED in order to determine the missing numbers?

If you want to solve the original problem yourself, you can go there and look for the rest of the problem and a discussion on finding the answers, but here is the set of numbers provided:

mean = 76;
range = 32; IQR = 21

. . . View This Fullsize

Insert parentheses into each of the following expressions so that each will have the same value.

\( 4 + 3 * 7 - 4\)

\(2 * 3 + 3 * 5\)

\(2 * 5 - \frac{1}{2} * 10 * 9\)

\(3^2 ÷ \frac{1}{3} + 3 * 6\)

. . . View This Fullsize

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?

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

. . . View This Fullsize

A Challenge from StandupMath:

Can you arrange the integers 1 to 17 so that each adjacent pair adds to a square number? 

Hey!

What if we didn't put them all in a straight line? What's possible if you do that?

. . . View This Fullsize

It's a well-known formula ... your age divided by two, and add seven. If your date is any younger than that, it's just creepy.

By this calculation, what is the youngest you are allowed to go on a date?