The moral of the toothpicks stories.

(First you have to read the blog below...this website puts the latest story on top and it will be hard to follow this story without reading the background on the first post below.)

So like i was saying, i try to select an honorable senior to go to the grocery story to get a box of 50 cent toothpicks with 250 Toothpicks on the box.

This senior has to be very honest because they can not add or delete any toothpicks after pulling it from the shelf. In fact i give them a roll of tape so they can seal the box until they get back to my school.

One year the president of the student body and eventual Yale student went to buy the box. He came back and i selected another senior to help him count the toothpicks on the floor while i continue with that day's lesson.

After a few minutes and most of the students watching the boys on the ground, they shouted we have 250 TOOTHPICKS !!! They were so proud and already claiming their prize of a six pack of cokes for the class.

But then i looked at the senior i had sent to the store. I said Ben, you know i have done this for 30 years and we have NEVER had exactly 250 toothpicks. Are you SURE ??

Ben started to turn RED....lol

I said i know you guys are just having fun, but we need to be truthfull here....not worth losing our honor over a silly little bet.

Then Ben sang like a canary.

There were actually 252 toothpicks and his buddy counting with him had pressured him into putting two away in his pocket.

All hell broke lose about the coke bets and such.

I said all best were off since there was some trickery going on with the toothpicks.

We also spent the rest of the class talking about honesty and peer pressure as they were getting ready to graduate and go to college. One of my best math lessons of the year.


(and the story continues !!)

So now i am with another class. These are juniors and we have no one to go buy a box of toothpicks. But i have kept the box of toothpicks from my first period and i have promised the students that i have not messed with the box.

Again i choose an honest and reliable junior (this time an all american volleyball player already signed to play for Stanford some day). And she and her friend begun to count the toothpicks on the floor.

I am teaching my lesson for that day when the volleyball player yells out:
"there are exactly 250 toothpicks in this box !!"

The class cheers as they think they have just won a six pack of cokes.

But i walk over and say, now that is not possible. Let me see your stacks of 10's.

I do notice one stack a little lite !!....there are only 8 toothpicks in that pile.

I exclaim, i only count 248 !!

At that point the all american volleyball player who i know is an honest person admits that she put 2 toothpicks in her pocket. She turns red as she produces the 2 toothpicks that they thought they had leftover from the count.

Now everyone is screaming about the bet and the cokes and who did what and when it was done, etc.

It just happened that the senior from the first period just happened to walk in to collect the attendance sheet. I quickly ask him, "how many toothpicks were in this box this morning ?"

He says 250 !!! (to my surprise...i thought we had had a very good discussion about honesty and so forth)

I said, yes, but we had 252 this morning !!

And he says, "I kept the 2 extra toothpicks in my POCKET !!" (bless his heart)

So again we finished the days math lesson talking about honesty and peer pressure and the such.

(I could not have made this up !! and Hollywood would NOT believe it....lol)

I also learned a valuable lesson because i would have bet $1,000 that there were more than 250 toothpicks in THAT box !! and at that moment there were only 250 !!
(since the senior from the first class had kept two in his pocket...dam shame)

Statistics 3 - The Toothpick Box

Every year when we get into the statistics part of precal, i ask the students:

"so how many toothpicks do you think there are in a box of toothpicks that says 250 Toothpicks" ?

Almost all the students yell 250 !! (of course, it says so on the box)

So now we make a few coke bets (diet coke for ME) and we send a responsible senior to the nearby grocery store to buy a box of 250 toothpicks.

Remember the movie Rainman ? with Tom Cruise and Dustin Hoffman ? Dustin Hoffman is autistic and Tom sells cars in LA. There father dies and Tom goes back for the reading of the will. The father leaves all the money to his older brother Dustin who is living in a special home.

Tom tries to take Dustin back to LA, but runs into all kinds of problems. One of them is that Dustin will NOT fly. Another is that Dustin has to see Judge Wabber every night at 7 pm on TV.

They are in a Diner, when the waitress drops a box of toothpicks and Dustin says "246". Tom says 246 what ? and Dustin says 246 again.

Tom looks at the toothpick box in the waitress hand and there are only 4 toothpicks left in the box, and the box says 250 on the cover. That means there are 246 toothpicks on the floor and Dustin somehow counted them as the fell or once they were on the floor. Autistic.

So Tom gets this great idea that Dustin can count cards, and they go to Vegas.

So again i ask the class:
"how many toothpicks are there in a box of 250 toothpicks" ?

And they all yell, 250 !!

When the responsible senior comes back we sit down and count the toothpicks. I have done this for over 30 years and sometimes with 2 or 3 classes a year.

WE HAVE NEVER COUNTED EXACTLY 250 TOOTHPICKS !!

We have actually gone over 250 only two times....the lowest i can remember was below 240.

You see a machine can NOT count exactly 250 toothpicks....for a machine to do that it would cost way too much (only machines that work with the space program are that accurate).

My data has shown a mean (average) of 246 and a standard deviation (SD) of 3. That means we should expect that 95% of the boxes should have between 252 and 240 toothpicks in them. (mean plus or minus 2 SD's)

It is strange that we have never gotten 250 exactly.