Valentine's Day Math

For fourteen years while I worked in Monticello, I loved coaching MATHCOUNTS at Piedmont Academy.  I’m one of those seemingly rare people who like working with middle school students.  They are young enough not to be too cool, but they are old enough that they are really starting to understand some things.  Maybe I’m just an overgrown 12-year-old myself.

Last March I began a new job in Macon, and with my commute, I’m not able to coach anymore, unfortunately.  (However, I’m so happy that I can continue as the Middle Georgia chapter MATHCOUNTS coordinator, which I have been doing since 1998.)  I look back very fondly at my years of coaching.  Over those years, I mostly used the MATHCOUNTS school handbook to coach my mathletes, but sometimes I came up with my own materials to highlight a particular theme.  One time we had a Pot o’ Gold scavenger hunt for St. Patrick’s Day, in which the students followed clues and solved math problems around the school.  Another time we solved greyhound math problems, and I brought in my own greyhounds so that the students could meet actual retired racing greyhounds.  Several times I dressed up as Madame Pi and “read” the students’ minds.  (This was actually a neat math trick.)  Once we even played Survivor, where the mathletes solved math problems as their challenges.

Since today is Valentine’s Day, I’ll share the Valentine’s math questions that I created one year for my mathletes.  (I’ll post the answers tomorrow.)

1) Edna and Ethel were running a kissing booth.  If Edna received twice as many kisses as Ethel, and together they received 111 kisses, how many kisses did Edna receive?

2) Letters spelling I LOVE YOU are written on slips of paper, one letter per slip.  The slips are placed in a hat, and one is drawn at random.  What is the probability of drawing a vowel?  Express your answer as a common fraction.

3) Cupid is target practicing with his bow and arrow.  His circular target has a radius of (QT)^0.5.  What is the area of his target.  Express your answer in terms of pi.

4) Forrest Gump is selecting 2 chocolates from a box of 12 chocolates.  If each chocolate is different, how many combinations of chocolates can he get?

5) Juliet wants to trick Romeo into thinking that she is dead, so she is getting a sleeping potion from the apothecary.  If she needs 1.5 ounces of potion per 25 pounds of body weight, and Juliet weighs 110 pounds, how many ounces of sleeping potion should Juliet purchase?  Express your answer to the nearest tenth.

6) The lower station of a cable car system is 2400 feet from the base of Lovers’ Leap.  2600 feet of cable extend from the lower station to the top of Lovers’ Leap.  If Sam simply jumps off of Lovers’ Leap rather than taking the cable car down, how much distance will he save?

7) At the Valentine banquet 10 women ate both hogs and quiches, but the 24 men ate only hogs because real men don’t eat quiche.  None of the women ate only hogs.  If 56 people attended the Valentine banquet, how many women ate quiches only?

8) Gary is considering going to the Sadie Hawkins dance, which is 10 miles from his house.  He can ride his bicycle 15 miles per hour.  Mary has invited him to the dance and will pick him up at his house on her bicycle-built-for-two.  If together they can ride 18 miles per hour, how many minutes will Gary save by going to the Sadie Hawkins dance with Mary instead of going stag?  Round your answer to the nearest minute.

9) Seven out of eight blind dates end up a disaster.  Of the remaining blind dates, three out of four couples wind up getting married.  If Helga gets set up on a blind date with Hagar, what is the probability that they will get married?  Round your answer to the nearest whole percent.

10) Buffy claimed that she would love Biff 4 Ever.  However, she broke up with him after only three weeks.  What percent of 4 Ever did Buffy actually love Biff?  Round your answer to the nearest whole number.

Second Ride in A Year of Centuries – A Benefit for MATHCOUNTS

Marvelous ride yesterday!  I did yesterday’s century for MATHCOUNTS in conjunction with the Peach Peloton ride.  It was the grand finale PP ride of the winter training season, going from Barnesville to Pine Mountain and back.  The planned route was 124 miles.  Because I knew I couldn’t hang with the PP guys for that long at their pace, I planned a slightly shorter route, which turned out to be 108 miles.  I rode with them for about the first 40 miles (more on that in a moment) and rode most of the remainder solo.  It was definitely a harder century for me than in January, but it was satisfying.

Rotations

I owe a lot to Chad Madan (Peach Peloton organizer) and some of the other veteran riders for teaching me how to ride in a group.  Riding in a group obviously is different from riding solo, but it’s also very different from racing in a group.  The point of a group ride is to be smooth, consistent, and predictable so that the group can stay together, except when there’s a designated attack zone.  For example, if you want to ride well together as a group, the front riders on the double pace line generally should exert less effort on the uphills and more effort on the downhills.  This might seem counterintuitive (and is opposite to race strategy), but it keeps the effort of the group more constant.

One training technique that we use during PP rides is rotations.  During rotations, the double paceline moves continuously in a counterclockwise direction.  When a rider on the right (closer to the white line) reaches the front, he/she moves to the left as soon as he/she clears the front rider on the left; he/she then begins to drift back toward the rear of the paceline.  The next rider on the front right executes the same move.  As each rider reaches the back of the paceline on the left, he/she moves to the right and begins pulling forward again toward the front.  In this way, the paceline keeps rotating counterclockwise.  The key is to continue doing this smoothly.

Rotations take more effort than regular double paceline riding, which can make them hard for the not-as-strong riders like me.  I’ve done plenty of rotation drills, but on a day like yesterday when I knew that I would need as much energy as possible, I opted to sit at the back during rotations.  If you sit at the back, you hang out behind the rotation on the left-hand side.  This isn’t as easy as lying on the sofa eating bonbons, but it does use less energy than taking part in rotations.  My original plan had been to ride with the group until the store stop in Shiloh at about mile 57, but about half way through rotations at about mile 40, I just couldn’t hang with the group any longer.  (The guys did rotations for about 15 miles!)  Getting dropped really wasn’t a problem.  I just wound up riding by myself a little longer than I had planned.  I tried to keep up a decent pace while enjoying the lovely scenery on this beautiful February day.  West central Georgia has some of the prettiest terrain in the state!

Store Stop

When I got to the store stop in Shiloh, I was pleasantly surprised to find the guys still there:

My Peach Peloton Peeps

They left before I finished my peanut butter and jelly sandwich and banana, but I’m glad I got to see them again before I split off on my shorter route.

The PB&J sandwich I had packed, rather besquished after being in my jersey pocket for 57 miles

From the store the guys headed west to ride the Pine Mountain ridge, and I went north toward Warm Springs.  (Warm Springs is the home of the Little White House, where Franklin D. Roosevelt spent much of his time when he was away from Washington, D.C.)

Detour

There was a detour in Warm Springs due to road construction.  The route was loaded into my Garmin bike computer, but it can be a little tricky to find the course again if you leave it.  The Garmin doesn’t show a real map, just a depiction of your current position and any imminent turns.  However, between my Garmin, the route that Chad Madan had uploaded onto his PP blog, and the mapping app on my phone, I got back on course.  Unfortunately, I added about two miles to my route by taking a slightly wrong turn!  At least I hadn’t gone too far before I realized that I was going north but needed to be heading east from Warm Springs.

Dogs

As much as I love dogs, they can be a real bane to cyclists.  Just ask my friend Bill Causey, who has had two serious crashes from dogs running into him.  Generally, I can tell if a dog is simply curious, more bark than bite, or a true threat.  Fortunately, most dogs do not fall into that third category.

After I had ridden several miles on the correct road leaving Warm Springs, I went past a house with dogs that started to chase me.  They were…killer attack Yorkies!  There were four of them.  They may have even had bows in their hair.  They did their best to defend their territory, yipping and running after me for about 10 feet.

Rest Stop

I kind of have to remind myself on these centuries that it’s not a race, particularly when I’m by myself.  So, I took a rest at about mile 75.  What a nice stop!  I sat in a grassy area by the side of the road and enjoyed the pretty view across the road:

I also ate a Clif bar and drank some water.  Hmm…I was getting kind of low on water…

Divining for Water

After another five or ten miles, I decided to get some water at the next available opportunity.  Churches can be a good place to refill.  There are tons of churches throughout rural Georgia, usually lots more than stores.  Often churches have an outdoor spigot.  I can’t imagine the church folks would mind giving a cup of water to a thirsty cyclist.  On the few occasions I have encountered church members when I was looking for water, they have always been extremely gracious.

On my current quest for water, the first church I came upon was Deliverance Tabernacle of Praise:

I would have offered praise of my own if they had delivered on the water – but no spigot.  So, I continued on my bicycle.  After only another mile or so, I approached Beulah Baptist Church:

Is this not the land of Beulah?  Apparently not – they had a couple of spigots, but the water was turned off.  I think this was a sign that I needed to pray for water…

After a few more miles, I saw a fire station – bingo!  If they hadn’t had water, I really would have been worried.  There were two very nice fire fighters relaxing at the station.  I asked if they had a spigot I could use.  They said that the water there had sulfur in it, and instead they gladly offered me a cold bottle of water.  Thank you Pike County Fire Department on Highway 109!  Y’all are the best!

Do You Carrot All?

I wasn’t much of a carrot because it was a matter of when, not if, the peloton would catch me before the end of the ride. They finally did with about seven miles to go.  I was glad to see them regardless, but I was especially happy that it looked like I would be able to catch onto the back for a little boost back to the parking lot.  The guys were taking turns with a regular double paceline.  For the first two pairs that pulled, everything was going fine for me.  I was very tired, but I felt like I was exerting about the same amount of energy with the faster group as I had been by myself.  Then, I was thrown into…The Stoney Grinder.

Stoney is a mo-chine of a rider.  He pretty much pulverizes everyone, and I don’t know if he even realizes it.  When he started pulling, I immediately knew he was there even though I couldn’t see exactly who was at the front.  I simply couldn’t keep up, and I dropped off the back.  Robert (sweet husband!) stayed with me for the few remaining miles.  Shortly thereafter, Chad Davies also hung back to accompany me, too.  The Georgia Neuro Century Escort Service rides again!

Wrap Up

Yea, I made it!  I was whupped, but I was thrilled to have finished my second century in A Year of Centuries.  I rode nearly 70 miles of that by myself, which was a big accomplishment for me.  I told myself several times during yesterday’s ride that since I made it through the long recovery period after my crash, I could do this whole ride.

As I rode, I couldn't help but think about rate/time/distance problems (r x t = d), which are fairly common in MATHCOUNTS.  Even more importantly, I also thought about all of the MATHCOUNTS mathletes who are competing in chapter competitions during February.  I hope that in the same way that I persevere through riding and training, they will persevere through the problems they face, whether in math or life.

P.S.

I had considered having some cycling MATHCOUNTS problems for the guys to do at the store stop, but Robert convinced me that I’m the only one in our group that really likes to solve math problems.  Even so, here’s a fun one that I know they all could get:

If John Cozart shows up for Tuesday Worlds, what is the probability that he rides wearing dress socks?  100%

STEM Jokes

An engineer, a physicist, and a statistician were out game hunting.  The engineer spied a bear in the distance, so they got a little closer.  "Let me take the first shot!" said the engineer, who missed the bear by three meters to the left.  "You're incompetent!  Let me try," insisted the physicist, who then proceeded to miss by three meters to the right.  "Ooh, we got him!!" said the statistician.

 

Q: Why did the chicken cross the Moebius strip?

A: To get to the other ... er, um ...

 

An evil psychiatrist kidnaps a chemist, an engineer, and a mathematician to see how their minds work.  He locks them in separate cells with a year supply of canned beans and leaves.  When he comes back in a year to check on his prisoners, he finds:

• The chemist had collected rainwater to corrode the cans of beans so he could eat them.

• The engineer had taken apart his bed and made a crude can opener out of the parts.

• The mathematician was slouched on the floor, long since dead. Written in blood beside the corpse read the following:

Theorem: If I don't eat the beans I will die.

Proof: Assume the opposite and seek a contradiction.

 

Two mathematicians went out to lunch.  Over lunch, one complained that most people don't understand even basic math.  The other took a more optimistic view.  A short time later, while the pessimist was in the bathroom, the other called the waitress over.  "I am going to call you over in a few minutes," he explained, "and I am going to ask you a question.  I want you to answer X³/3.  OK?"  When the pessimist came back, he called the waitress over.

"Look, I'll prove people understand math better than you think.  OK, young lady, what is the integral of X²?"  "X³/3" she slowly repeated and walked away.  Then she turned around and said, "Plus a constant."

 

An engineer, a physicist, and a mathematician are trying to set up a fenced-in area for some sheep, but they have a limited amount of building material.  The engineer gets up first and makes a square fence with the material, reasoning that it's a pretty good working solution.

 

"No, no," says the physicist, "there's a better way."  He takes the fence and makes a circular pen, showing how it encompasses the maximum possible space with the given material.

Then the mathematician speaks up: "No, no, there's an even better way."  To the others' amusement he proceeds to construct a little tiny fence around himself, then declares:

"I define myself to be on the outside."

 

 

Engineers want to be experimental physicists.

Experimental physicists want to be theoretical physicists.

Theoretical physicists want to be mathematicians.

Mathematicians want to be philosophers.

Philosophers want to be theologians.

Theologians want to be engineers.

 

My mother is a mathematician, so she knows how to induce good behavior.  "If I've told you n times, I've told you n+1 times...."

 

An engineer, a physicist, and a mathematician were traveling through Scotland when they saw a black sheep through the window of the train.

 

"Aha," says the engineer, "I see that Scottish sheep are black."

 

"Hmm," says the physicist, "You mean that some Scottish sheep are black."

 

"No," says the mathematician, "All we know is that there is at least one sheep in Scotland, and that at least one side of that one sheep is black!"

 

A mathematician wandered home at 3 AM.  His wife became very upset, telling him, "You're late!  You said you'd be home by 11:45!"  The mathematician replied, "I'm right on time. I said I'd be home by a quarter of twelve."

 

Teacher: "What is seven Q plus three Q?"

Student: "Ten Q"

Teacher: "You're Welcome."

 

An architect, an artist, and an engineer were discussing whether it was better to spend time with the wife or a mistress.  The architect said he enjoyed time with his wife, building a solid foundation for an enduring relationship.  The artist said he enjoyed time with his mistress because of the passion and mystery he found there.  The engineer said, “I like both.”  “Both?” the others asked.  The engineer replied, “Yeah.  If you have a wife and a mistress, they will each assume you are spending time with the other woman, and you can go to the lab and get some work done.”

Solution to Groundhog Day Math Problem

Beau would chuck 15 cords of wood.  Phil would chuck 5 cords of wood.