[UPHPU] The Lost Sheep Challenge

Orson Jones orson.uphpu at bookstore.usu.edu
Tue Oct 2 20:47:38 MDT 2007


Justin Giboney wrote:
> You could go through and add every number you come across and subtract
> that from the total you would get if they were all there, and the number
> that is left would be the one missing.

Funny, I just recently overheard someone explaining how to answer part
of this question. How to calculate 1+2+3+...+98+99+100
It went something like this.

It is a bit easier to add those up if you do it twice.

  1 +  2 +  3 +...+ 98 + 99 + 100
100 + 99 + 98 +...+  3 +  2 +   1

Rather than adding across left->right, add each column
100+1=101, 99+2=101, 98+3=101...
So, you have 100 sets of numbers that add to 101.
Multiply 100*101 then divide by 2 (you added them up twice)

Sometimes math can be really interesting. (When it doesn't take an
entire page to explain a problem.)

>>> You have 100 sheep in a flock and they are all numbered. Each has an
>>> identification tag with a number -  1 through 100. One of them is
>>> lost. Other sheep are scattered over the pasture and cannot be
>>> examined in sequential order of their numbers. Come up with a method
>>> that would allow you to quickly identify the lost sheep. The use of a
>>> simple arithmetical calculator is allowed. The use of a pen or any
>>> other note-taking instrument is not (to disallow the trivial but
>>> unscaleable roll-call method).


Or, if you have a short rope on each sheep and a long horizontal pole:

Take each sheep and tie it with a loose but secure knot to the middle of
the pole. Take the next sheep and tie it to the left of that sheep if
its number is smaller or to the right if its number is larger. Proceed
to sort each sheep to its position on the pole in the same manner.

When done, walk along and note any missing numbers.

Fun question to get creative with.

Orson


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