## Friday, March 15, 2013

### Lost Teeth Puzzle

Teeth is an important topic of discussion in our home. Our 12-year old son recently lost his tooth in ... a swimming pool. Our 9-year old daughter keeps counting her lost teeth, wiggly teeth and growing teeth.  Every few month she goes on an ice-cream diet because everything else just hurts too much when your wiggly tooth is hanging on a muscle thread. And our 1.5-years old finally got her first four teeth to cut and chew a grownup food but is drooling, sucking and crying while another one is growing.

My husband and I are doing pretty well with our teeth this year but this may very well be because our dentist died... and we haven't found a new one yet to tell us what is wrong with our teeth.

So, an easy puzzle for tooth owners of all ages.

My 10-year old daughter came to me telling that she was trying to count how many teeth she has lost overall.  But every time she counted she got a different number: 16, 17, 13, 15. She was asking what is the actual number of teeth she lost. Can you help her produce the best estimate from these numbers?

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Dennis (of Dennis and Katrina) said...

Well, we can start with the mean: 15.25. We can tell her that 15 teeth is a good estimate.

Or, we could go a bit further, and calculate the standard deviation: 1.70783. With the standard deviation, we can generate confidence intervals.
- A 90% Confidence Level gives us 13.243 to 17.257 (13 to 17 teeth)
- A 95% CL gives us 12.535 to 17.965 (12 to 18 teeth)
- A 99% CL gives us an even wider range, and would be kind of silly!

Or, we could check with the American Dental Association (ADA) [http://www.mouthhealthy.org/en/az-topics/e/eruption-charts.aspx] and learn that there are typical age ranges for primary teeth loss. Based on being 10 years old, I would estimate that she has lost approximately 14 teeth.

Anonymous said...

I would throw out the high and low ones. That leaves 15 and 16. However, since the gap between 13 and 15 but none between 16 and 17, I would go with the lower number, 15.

Gurubandhu

anne-marie said...

There is no outliers so I will use the mean.
(15 + 17 + 13 + 16)/4 which is 15 teeth

Jerome said...

Assume she's 10 and not 9.
Assume that she is not ready to shed her teeth is she is on the cusp.
Use this reference

http://comfortdds.com/dentist-lafayette-in/dentistry-by-stage/tooth-schedule/

Lower Teeth (Shed)
Shed
central incisor (2)
lateral incisor (2)
first molar (2)
Total 6

Upper Teeth
Shed
Central Incisor (2)
Lateral Incisor (2)
First Molar (2)
Total 6

From this I would say 12. Since the closest number is 13, that's my guess.

Note this is just a guess. I know nothing about how teeth go out (like in pairs) or if I should be taking ratios if her age is in the range where she could be getting a tooth or not. What I mean is if the range is 9 to 12, should I add 1 tooth or not? I have not, but that does not say I am correct.

========
I find it interesting that the mouth goes from 20 teeth to 28 teeth.

I wonder if you can tell enough of a difference between baby teeth and adult teeth just to count the adult teeth. If you get a total over 20, that is not a replacement amount.

Jerome's wife said...

I added 16, 17, 13 & 15 which totaled 61 and divided by the number of guessed losses of teeth, which was four (guesses). So 61 divided by 4 will give an average of 15.25, ...so to be more general I would say she lost 15 teeth overall.

Anonymous said...

I think that your daughter has probably lost 15 or 16 teeth, and my best estimate guess would be 16 since it can be hard to distinguish where one teeth ends and another starts sometimes.

The mean of 16, 17, 13, and 15 is 15.25
The median of 16, 17, 13, and 15 is 15.5
If you throw out the outlier count (13) here and it does seem likes it's probably too low, then the mean and median would be 16.

Btw, how much does the tooth fairy pay in your house? :)

TracyZ

Maria said...

Oh I just love your answers. The power of a group where everyone thinks separately without being biased by others' answers.

We have:

1)the mean (16+17+13+15)/4 = 15.25

2)the median (place all the counts in order and pick the middle) we have 13, 15, 16, 17. middle is between 15 and 16, say 15.5

3)estimation from the America Dental association or other Dentas site based on age - 12 to 14 teeth

4)take outliers away and then compute a mean. but among 13, 15, 16 and 17 there are no outliers, so same answer as in 1.

5) go to a dentist and ask whether she/he can distinguish between baby and grownup teeth and count how many are actually lost

Very nice!
By the way I did list my daughter as 9 and then 10 years old. She is 9 till April 5th but it is almost 10!
And just as I used this opportunity to explain to my daughter what a mean, median and outliers are, my son came home with another interesting example.

He is on his school's orienteering team. We haven't succeeded in making him like hiking but just a few months at school and he got hooked on running around with a compass. Last week he came home from a competition and told me that he did badly - he fell, roll down a hill, got all scratched. But his 10-person school team got 3rd place overall. I asked how the score was counted so that his bad performance didn't influence the team. He told me that they counted the score of a 6th best person in each team as a team;s score. A median!

Puzzle point for everyone who answered.

Jerome said...

I noticed Tracy Z asked what the Tooth Fairy Rate was. In my day it was 25 cents a tooth. Anybody got a current number? I'll bet 25 cents wouldn't buy a tip of the root.

Jill said...

It would be better to decide which ones still need to come out and subtract from 20 but I would estimate the mean of 15.

Unknown said...

my guess is 14

Prateek said...

My guess will be 17.
As, every time she counts a different number. This is because even if she lost some teeth and then get the new ones which are exactly the same as old once. So she got confused and missed some of the teeth. So, my guess will be the maximum of the given number.