# Can you make 147?

Last week I was in a high school algebra classroom and the teacher was helping students get back into the swing of the school year and doing mathematics.  He was playing a game with the students in which he would display a number using a random number generator and the students would have to use all of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 as well as operations and grouping symbols to equal the number displayed on the screen.

For example, if the random number generator produced the number 17 a winning answer could be

17 = (4)²+1+((3+5+6+7+8+9)0) = 16 + 1 + 0 = 17

The first team to figure out a way to represent the number got 5 points.  If another team could represent the number in a different way they earned 2 points.  If a team checked another answer and found an error, they earned a point also.

The game was exciting!  It was loud!  People were yelling about the order of operations and exponents!  They were challenging each other about math!  It was music to my ears!

Then, the random number generator displayed the number 147.  It started off like any other round . . . whispering, writing, stopping, writing some more . . . and then something interesting happened–no one could figure out a way to combine the 10 digits to get the number 147.

I left that day thinking about the number 147 . . . was it impossible to generate the number using all 10 digits?  If so, how many other numbers could not be generated using this method also?  As I was driving back to my office I began thinking about the properties of 147.  First, I wondered is 147 prime?  But I quickly figured out that is was not prime (I used the test for divisibility by 3–1+4+7=12, which is divisible by 3, so 147 is divisible by 3).  The prime factors of 147 were 7 and 3, in fact 147 = 7²(3).

Now I had a strategy!  Was there a way I could combine 10 digits to equal 7, 7, and 3?  If so I could represent 147 in the way that was so tricky!  Guess what?  I could!  And now its your turn!  Show me how you represented 147!  Can you do this in a way that doesn’t build off of the prime factorization of the number?  Good Luck!

Want to recreate this activity yourself?  Here’s a random number generator.  Want to learn more about divisibility tests?  Look here. And you can find a related post here. Or here.

# What’d you do this summer?

Now that school’s back in session, I’m sure you’ve been answering the question “What’d you do this summer?”

We had lots of fun this summer, but one of the things I’m most proud of is my hike up Deer Mountain at Rocky Mountain National Park!

My first experience with hiking anything other than flat land was this winter in Palm Springs, CA when my husband and I hiked through various canyons.  I must say I felt like quite the outdoors-man (or woman) on those hikes and the views were spectacular!

When we booked our flight to Denver for this summer I declared almost immediately that we would be hiking through Rocky Mountain National Park just like we had hiked the canyons.

After getting a recommendation to hike Deer Mountain we were off . . . and 15 minutes into the hike I thought I was dying!

“Can we slow down?” I’d huff while my husband trudged ahead.

“Wait . . . feel my heart, its racing!” I’d worry while trying to keep up with his strides.

and finally, “What is wrong with me!  This mountain is crazy!”

We hiked the mountain in a little under 2 hours and 15 minutes (not including our 30 minute lunch at the top where we enjoyed the views and chased ground squirrels away from our crackers).

When we finally got back to the car I pulled out the mountain statistics:

Starting Elevation: 8940 feet

Highest Elevation: 10013 feet

Round Trip Distance: 6.2 miles

Hello?!? No wonder I was out of breath.  I’m used to living at an elevation of 668 ft., so before we even took off up the mountain, I was already 8272 feet higher than I was used to!

Then, we took off like crazy people!  From my point of view there are two ways to measure the reason I thought this mountain climb was so hard . . . the first is the slope of that darn mountain trail must have been really high!  Or, the speed at which we were walking up the side of that mountain was much, much too fast to really enjoy the scenery.

What do you think?  Steep slope?  Fast walking?  Or just out of shape mathematician?