this post reminded me of an old puzzle:

If you take one pill every half hour, how many will you take in one hour?

this post reminded me of an old puzzle:

If you take one pill every half hour, how many will you take in one hour?

I use this counting on daily hospital rounds. In surgery we keep track of Hospital Day (HD) and Post-Op Day (POD) for our patients. HD is a fencepost count and POD is a measure of the interval from the day of operation.

@andrew: Interesting puzzle – depends on whether you count 1:00, 1:30 and 2:00 as belonging to the same hour

@Brian: Cool, thanks for the real world example!

Also depends on when you take your first pill:

If you take a pill at 1:00, then in the hour 1:01 to 2:01 you will have taken just two pills.

[…] I just discovered BetterExplained.com, the brainchild of Kalid Azad. It’s great! Kalid writes clear, thorough explanations of all kinds of ideas from simple stuff to complicated stuff. Math, computers, marketing, communication and more. […]

Finally, a clear way explanation of why 1 Jan 2000 was not the beginning of the new century (and millennium) - 1 Jan 2001 was!

I’d like to add one more thing here…

Consider cutting a cake into 10 pieces ?? How many times do you need to cut; it’s 9.

Are you sure? I think I can cut a cake into 10 pieces with just 5 cuts.

Another real-world example:

Suppose you are designing a 10’ high stairway with 6" high risers and 12" wide treads (a ratio of 1:2). What is the length of the stair? You might think it would be 20’ (twice the height).

But look:

The stair will have a total of 20 risers (20 x 6" = 120" = 10’-0"). However, the stair only has 19 treads, so the total length of the stair will be 19’ (not 20’)!

When measuring the height of the stair, the risers are “spans.” When considering the length of the stairway, the risers become the “fence posts”, with the treads being the spans in between.

I’m an architect, and I still have to make myself a little diagram to figure this out on each new project!

Mikekoz-

I think you can also cut a cake into 11 pieces with just 4 cuts. These would be strange pieces, of course!

Hi Kalid,

just wanted to say that I have been following your posts through RSS for a while now and find them really useful. You have an excellent way of communicating the essence of an idea/concept distilled to its base units. This explanation on counting is something that many people notice, but few can annunciate well. Thanks.

@Alexander: Thanks for dropping by and for the comment. I really want to break things down to their simplest elements, so I’m glad it’s coming through! I think most concepts have a simple essence, but often times we try to jazz it up to make it seem more “impressive” :).

[…] Learning how to count (avoiding the fence post problem) […]

Great post, as usual.

This is related to the puzzle:

On a typical Wednesday, how many times does the minute hand pass the hour hand?

The answer is probably not the first thing that comes to mind–or the second. This puzzle takes the fencepost problem to a new level.

[…] Learning How to Count (Avoiding The Fencepost Problem 28 Apr 2009. Working from 8 to 11 means you are covering the spans 8-9, 9-10, and 10-11. 8 to 11 means a "time" of 3 hours. Seconds: I start a race, and the start time at 12: 01:08 (12 hours. Try a simple example (a fence 10 feet long) to test if you' ve. Pingback by how to count « a Silent Parrot — March 4, Learning How to Count (Avoiding The Fencepost Problem […]

[…] 8.Learning How to Count (Avoiding The Fencepost Problem) | These points can be houses, floors, or plain integers. Whatever they are, they’re labeled so we can count them easily. 1 to 10 means ten items. … Pingback by Topics about Aprils-day » Learning How to Count (Avoiding The Fencepost Problem … — April 28, 2009 @ 6:58 pm… http://betterexplained.com/articles/learning-how-to-count-avoiding-the-fencepost-problem/ […]

Thanks for this amazing article! My kids and I have noticed this come up in the past and we didn’t know there was a name for it. I’m going to put it up on the whiteboard in out family room and I’m sure they’ll be fascinated by it.

@Rebecca: Awesome! Yes, sometimes even just having a name for something makes you aware of it (when I’m counting things, I always double check to make sure I’m not off by 1, because I know of this problem :)). I’d love to know how your kids take to it.