Upward Bound Math 2 (Enrichment)

Is it possible to find a path that crosses all 7 of the bridges of Konigsberg exactly one time?

• Yes, it was possible

• No, no path was possible

Is it possible to find a path in this graph that uses

each edge exactly one time?

• Yes

• No

Which statement below is TRUE?

(Remember: An Eulerian Path is a route that uses each edge exactly one time. It's okay to revisit a vertex.)

• Graph 1: Eulerian path is impossible

  Graph 2: Eulerian path is possible

• Graph 1: Eulerian path is impossible

  Graph 2: Eulerian path is impossible

• Graph 1: Eulerian path is possible

  Graph 2: Eulerian path is impossible

• Graph 1: Eulerian path is possible

  Graph 2: Eulerian path is possible

An Eulerian circuit is a path that starts and ends at the same vertex and only uses each edge one time.

Is an Eulerian circuit possible for this graph?

• Yes, all the vertices have an even degree, so a circuit is possible.

• No, one of the vertices has an odd degree, so a circuit is not possible.

• Yes, all of the vertices have an odd degree, so a circuit is possible.

True or false?

It is possible to color any map with only four colors.

• True
• False

Factorial:

What is the value of 4!

• 4

• 12

• 16

• 24

Using a calculator or the formula for permutations...

How many ways can 1st, 2nd, and 3rd place

be awarded to 8 runners?

• 6

• 336

• 120

• 6720

Using a calculator or the formula for combinations...

How many ways can you make a 3-topping pizza

from a list of 8 toppings?

• 56

• 336

• 12

• 120

Statisticians prefer to use confidence intervals to predict an unknown average

than to pinpoint a specific number.

• True
• False

Which statement is TRUE?

The confidence intervals we calculated in class...

• ALL of our confidence intervals found the population mean

• MOST of our confidence intervals found the population mean

• NONE of our confidence intervals found the population mean