- #1
konartist
- 47
- 0
Can you count and add all the numbers 1-100 without using a calculator?
Challenge Yourself: Count and Add 1-100 Without a Calculator!
- Context: High School
- Thread starter konartist
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Discussion Overview
The thread discusses the challenge of counting and adding all the numbers from 1 to 100 without using a calculator. Participants explore various methods and historical anecdotes related to this mathematical task.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- Some participants suggest that it is possible to add the numbers 1 to 100 without a calculator, referencing historical anecdotes about Gauss.
- One participant mentions using the formula for the sum of an arithmetic series: sum = 0.5n(n+1), leading to the conclusion that the sum is 5050.
- Another participant elaborates on the pairing method, explaining how to group the numbers to arrive at the same sum of 5050.
- There is a discussion about the average value of the numbers, with some participants clarifying that 50.5 is the average of the first and last terms in the sequence.
- One participant expresses confusion about the average value and its calculation, prompting further clarification from others.
- A participant provides a link to a lecture that explains the method used to sum the numbers.
Areas of Agreement / Disagreement
Participants generally agree on the methods to calculate the sum of the numbers, but there is some confusion regarding the average value and its significance. The discussion includes multiple viewpoints and clarifications, indicating that not all participants are on the same page.
Contextual Notes
Some participants reference historical anecdotes and mathematical formulas without fully resolving the nuances of their explanations. There are also instances of miscommunication regarding the average value and its calculation.
- #2
kant
- 388
- 0
konartist said:
You got me!
- #3
VietDao29
Homework Helper
- 1,424
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As a metter of fact, I think I can 
If I am not mistaken then Gauss did it centuries ago...
If I am not mistaken then Gauss did it centuries ago...
- #4
davee123
- 671
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konartist said:
Let's hope not! ... Maybe all the *integers*, tho :)
(And yeah, you can use the old ((S+F)/2)*(F-S+1) trick to add all the integers between S and F)[/color]
DaveE
- #5
Jimmy Snyder
- 1,137
- 21
Well it wasn't easy, but there are 100[/color] of them.konartist said:
- #6
konartist
- 47
- 0
VietDao29 said:As a metter of fact, I think I can
If I am not mistaken then Gauss did it centuries ago...
Yes sir, an old wive's tale is that he one day was punished in 3rd grade class and the teacher asked him to add all the numbers 1-100 thinking it would keep him busy, but he was able to reply the answer back to her in a matter of seconds.
- #7
michealsmith
- 124
- 0
yea u just use the formula...sum = 0.5n(n+1)
so 0.5 x 100 x 101 =50 x 101 = 5050
so 0.5 x 100 x 101 =50 x 101 = 5050
- #8
AKG
Science Advisor
Homework Helper
- 2,561
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Yes, 1 + ... + 100 = (1 + 100) + (2 + 99) + ... (50 + 51) = (101) + (101) + ... + (101) [50 times] = 50 x 101 = 5050. I heard that this is how Gauss did it.
- #9
Cybersteve
- 32
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So what you're all saying is, find the average value (50.5) and mutiply by the number of terms.
- #10
mattmns
- 1,129
- 5
What is 50.5 the average value of?Cybersteve said:
- #11
VietDao29
Homework Helper
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I think he meant the average value of the first term and the last term, ie:mattmns said:
(1 + 100) / 2 = 50.5
- #12
Cybersteve
- 32
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mattmns said:
50.5 is the average value of all the numbers 1 to 100 inclusive.
If there were an odd number of terms in an evenly spaced sequence the average would be the middle term.
As this sequence is even the average value is the average of the two middle terms - 50 & 51.
- #13
mattmns
- 1,129
- 5
Ahh, I must have misread something.
- #14
Jimmy Snyder
- 1,137
- 21
Not so much misread as partially read. 50.5 is not only the average of 1 and 100. It is also the average of 2 and 99, 3 and 98, etc. That is, it is the average of the set of integers from 1 to 100.mattmns said:
- #15
Zygotic Embryo
- 29
- 0
im lost...
- #16
Mk
- 2,040
- 4
This is easy.
Here is a lecture that shows you how to do it.
http://www.jimloy.com/algebra/gauss.htm
Here is a lecture that shows you how to do it.
http://www.jimloy.com/algebra/gauss.htm
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