Brain Teasers
A History Lesson
When Carl Friedrich Gauss was six years old (back in 1783), his schoolteacher asked the students to add up all the numbers from 1 to 100. Unfortunately for the teacher, who was hoping to keep the class occupied, it took young Gauss only a few seconds to work out the answer. Can you figure out what Gauss did to come up with the answer?
Hint
There is a pattern...Answer
Gauss realized that the series 1+2+3+4...+97+98+99+100 could be written as 1+100+2+99+3+98+4+97... or 101 times 50 to get the total 5,050.This trick works for any sum of sequential integers. The general formula is n(n+1)/2, which is the equation for triangular numbers.
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I saw this teaser in the book, "Lateral & Crtical Thinking".
I saw this teaser (word for word) in Ivan Moscovich's Playthinks book, but I see he also plagiarized other people's teasers too.
Ouch, some copying and pasting must have gone on. Be orignal next time.
maybe it is plagiarism, but i have seen this puzzle in several places and did not see it on this site, so i wanted to share it. sorry
toast9897, I'm sure that someone here had not seen that brainteaser before, and that by submitting it, you've given them some fun, so don't sweat it. At least you admit that it's not original - some people here would no even do that.
I dont see anything wrong with repeating teasers from somewhere else if you think most people haven't seen it or maybe someone will enjoy seeing it again.
I actually have a different solution for this particular teaser because when I was taking a high school computer class way back in the early 80's we had to write an original program in basic. remember basic? This was the first program I had ever written on my own and it worked by taking any number you entered and it totalled the sum of the intergers from 1 up to that number. 1+2+3....+n=? The program was essentially the formula n(n+1)/2 or take your number, multiply by the next highest interger and divide by 2, which I am proud to say I discovered all by myself at the tender age of 15. To be honest I have never, to this day, looked to see if this formula is actually contained in a common math text book, but it works. I figured it out by starting with 2, 3, 4, and so on, adding the whole numbers from 1 to each number and looking for a pattern until I saw it. It only took about 5 minutes and that formula has stuck with me ever since.
So you see, I would have answered the teaser by either saying he knew the formula or figured it out just like I did.
Oh BTW: 100 x 101 = 10,100
10,100 / 2 = 5,050
Still works! right?
I actually have a different solution for this particular teaser because when I was taking a high school computer class way back in the early 80's we had to write an original program in basic. remember basic? This was the first program I had ever written on my own and it worked by taking any number you entered and it totalled the sum of the intergers from 1 up to that number. 1+2+3....+n=? The program was essentially the formula n(n+1)/2 or take your number, multiply by the next highest interger and divide by 2, which I am proud to say I discovered all by myself at the tender age of 15. To be honest I have never, to this day, looked to see if this formula is actually contained in a common math text book, but it works. I figured it out by starting with 2, 3, 4, and so on, adding the whole numbers from 1 to each number and looking for a pattern until I saw it. It only took about 5 minutes and that formula has stuck with me ever since.
So you see, I would have answered the teaser by either saying he knew the formula or figured it out just like I did.
Oh BTW: 100 x 101 = 10,100
10,100 / 2 = 5,050
Still works! right?
Apr 02, 2004
yeah, i also saw this problem in a geometry book we used. good problem, though.
It doesn't bother me if you found it in a book or on the bathroom wall. Just try to switch names and other little things in the teaser so that your not getting credit for the authors work. Just a fair thing to do. Otherwise, it's a great teaser!
This is hardly a teaser; it is exactly what it says it is - a piece of Mathematical history that can be found in hundreds of Mathematical Textbooks. It certainly can't be called plagiarism because it cites the source - a true story about K F Gauss.
I see this as blatant plagiarism. Have a look at "A Mariner's Chance" (teaser number 17169) also submitted by toast9897. This teaser and its answer was also copied word-for-word from the same book by Ivan Moscovich. "A History Lesson" is the title of the teaser, not citing the source - that would go something like "I found this in the book Playthinks". Perhaps toast9897 thought that my previous comment was a license to plagiarize. "The Mariner's Choice" teaser is just begging to be translated into another teaser. Spacemen, frogs, football punks, cats anything else could be substituted for the sailor, and the teaser re-worked. Then it would certainly not leave such a bad taste in my mouth. I still think it's fine to repeat teasers that you have read or heard elsewhere - just give credit where it's due.
could we please drop this plagiarism subject? i see no reason to continue. we have established that 2 of my teasers came from playthinks, which is a wonderful book. several ppl have not read the book, and i think sharing a few is not going to harm the other 998 in the book. i have heard both of them before, and playthinks reminded me. so, how about no more plagiarism and no more insulting me. and i thank everyone who got my back on this.
That Carl is pretty smart to know that much.
I thought it took him 15 minutes, not a few seconds.
cool teaser. . it's about time that we get some real mindworking teasers. keep it working.
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