## Histogram Puzzles

In this exploration you will solve some histogram puzzles: Given a histogram, you will change bin widths and starting values to determine the data set it represents.

### Sketch

This sketch shows the histogram of ten data points that are hidden. The data points are integers with values in the interval from 0 to 30. Your challenge is to determine the values of all ten data points.

You may adjust the histogram's starting value S and bin width W. The histogram will be updated dynamically. Continue to slide these two points until you believe that you know all the data points. You can use any number from 1 to 30 for S and any number from 5 to 10 for W. Each data point on a boundary between two bins is put into the bin on the right.

Press Show Data to see the solution or press New Puzzle twice to get a new puzzle.

### Investigate

1. See how many data points you can determine. Then press Show Data to see the data points and check your answer.
2. Press New Puzzle twice to get a new puzzle. You can do as many puzzles as you like.
3. How can you determine the smallest data value? The largest?
4. Which do you find more helpful, adjusting the start value or the width value? Explain.

### Sketch

This sketch is like the one above, but now there are 20 data points whose values range from 0 to 40.