## Ask Professor Puzzler

Do you have a question you would like to ask Professor Puzzler? Click here to ask your question!

Someone told me that "most people have a higher than average number of bones in their body." That doesn't even make sense to me. How can *most* people be above the average?

Whoever told you that is probably not right, but I'm pretty sure I know what they were reasoning. So first I'll explore their reasoning, and then I'll present an alternate view of the statement.

You see, the 'normal" human has 206 bones in their body, but the *average* number of bones in the human body, if you were to take a survey of all humans currently alive in the world - is *slightly less than 206*.

Why? Because some people were born without arms or legs. Others have had limbs amputated. So if you average the number of bones of all the people in the world, you'll end up with a number slightly lower than 206.

Let's just make up some numbers, so you can see what I mean.

We'll say that the population of planet earth is 8 billion people. Of these 8 billion people, we'll hypothesize that 0.5% of them have lost a limb (rough estimate based on the number of people in the U.S.A. with amputations), and that limb loss has cost them 30 bones (I'm completely making that number up).

So we have 7,960,000,000 people with 206 bones, and 40,000,000 people with 176 bones. How many bones is that in total?

7,960,000,000(206) + 40,000,000(176) = 1,646,800,000,000

That's a lot of bones! So to find the average number of bones per person, we divide by our 8 billion figure: 205.85.

Since *most *people have more than 205.85 bones, most people have a higher than average number of bones in their body.

Okay, so that's the reasoning your friend was using. But it's not quite right. Because, you see, when you are *born* you have about 300 bones in your body. These bones are connected by cartilage, and will eventually fuse together (the process by which cartilage turns to bone is called "ossification"). How long does it take this process to complete? Well, I don't know for sure. One site I looked at said the process is complete around the age of 20, another said 25. I didn't feel like tracking down more research on that, so let's go with the smaller number, and say the process is done at age 20.

*This is important: I'm attempting to prove your friend wrong, which means that at every step, my rounding is going to be done in the direction that *favors *your friend's hypothesis. Because if he's wrong in the best-case scenario, then we know he's wrong for sure!*

Now, I have no idea how many bones a child has at various ages, so here's what I'm going to do. I'm going to assume the best case scenario - every child under the age of 20 has 1 extra bone, leading to a huge chunk of the population having 207 bones instead of 206. Again, I know that I'm lowballing this massively, but my goal is to give your friend's hypothesis the benefit of the doubt.

So now we have to rework our numbers, and for this, I'm going to use 25% as the percentage of people in the world under the age of 20. This number is not completely out of my hat - I based it on some numbers for U.S.A. population, and rounded down a bit.

In our previous calculations, we had 1,646,800,000,000 bones, but now I want to break it down by adult vs. child, so I'm going to multiply that by 0.75 (75%) to get the number of adult bones:

Adult bones = 1,646,800,000,000(0.75) = 1,235,100,000,000

For children's bones, we'll take the total in our previous calculation and multiply it by 0.25 (25%). However, this number is based on 206 bones per person, so we're going to then divide by 206 and multiply by 207. This number isn't going to come out even, so we'll round down, in fairness to your friend's hypothesis.

Child bones = 1,646,800,000,000(0.25)(207)/206 = 413,700,000,000.

Now let's add the adult bones and child bones together: 1,648,800,000,000. This is only slightly larger than the other number we obtained (because I did so much rounding down), but it's enough to put us on the other side of 206:

1,648,800,000,000/8,000,000,000 = 206.1

So it turns out that most people (the adults without amputated limbs) have a *below average *number of bones. Bear in mind that some of these numbers I pulled out of a hat without a lot of research, but I think it's safe to say I lowballed enough numbers that we can be reasonably sure of the conclusion. If you disagree, drop me a note with your reasoning!