Techniques for Adding the Numbers 1 to 100

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81

Can anyone solve or write any algorithm for the follwing one.

Split the natural numbers in to two sets whose summation should be equal.

For example
Say the numbers range from 1 to 12 into two sets as follows whose sum is equal
1+5+9+4+8+12 = 39
2+6+10+3+7+11= 39

Can anyone derive formula for this. The above logic works only for the following conditions else it will fail

Condition 1 : When n((n+1)/2) is Odd not applicable only applicable when the sum is even

Condition 2 : When the number that needs to be split in to 2 sets are increasing uniformly or a series of number starting with 1.

Question 1 : Derive a formula for a number in the type series

Question 2: Derive a formula for a number which is in random fashion as below.
1,50,24,25,3,2

Awaiting for the reply GUYS!!!

82

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83

[…] Euler helped a lot) is to substitute the formula for adding a series of numbers (also explained here) and change 3 to our variable “num”: num * p * (p+1) / 2. That’s it! Now we have […]

84

[…] to add up all the numbers between 1 and 100 in order to keep him busy. Naturally Einstein found a quick way to do it and we can use his […]

85

how do you add like 1 to 49 for example is it the same pattern like the n(n+1)divided by two used for 1 to 100? and thanks for the info

86

[…] pois foi postulado por Gauss (e várias demonstrações do porque podem ser encontradas aqui) que a somatória dos n primeiros números pode ser escrita da seguinte maneira: Logo, temos a […]

87

You could work it out by turning it into an arithmetic sequence.

Using Sn=n/2[2a+(n-1)d]; where:

n = number of values
a = first value
d = difference between values

n = 100 a = 1 d = 1

S100=100/2[2(1)+(100-1)1]
S100=50[2+99(1)]
S100=50[101]
S100=5050

Easy Peasy!

88

the sum from a to b is:

(b-a+1)(b+a)/2

89

I look at it this way - 1+2+3+…+98+99+100.
If sum the first and last digits we get 101. Again if we sum the second and the last but one digits we get 101. This goes on till the midpoint 50+51=101
Considering 100 as n if we look at the series there are n/2 pairs of n+1. This matches Gauss’s formula.

90

@Nirmal: Yep, that approach definitely works. The only thing that’s tricky is counting how many pairs… what if you wanted to add 1 to 99?

91

Great but wat is u wanted 2 add up 2 99 not 100???

92

MATHS IS WANK!

93

Better yet, just use X as the number you’re adding to. So if you’re doing 1+2+3 all the way to 100, make x 100 and use this equation.

x(1/2x+.5)

94

[…] formula for adding up a series of numbers (1 + 2 + 3 + 4…) is very close to n^2/2, and gets closer as the number of steps […]

95

[…] Book launch 2009 034 | $1000 to 1 Million in 80 daysTechniques for adding the numbers 1 to 100 | BetterExplained […]

96

2,6,14,18,22,26,30,34,38 use any 5 nubers to get 100? pls give me the answer.

97

[…] if you remember the Gauss anecdote, you can do it even simpler by using a variant of the […]

98

I made up a similar equation that will also do the summation of the series. It was:

sum = ((N / 2) * N) + (N / 2)

What is weird is that you can not do:

sum = (2N / 2) + (N / 2)
sum = N + (N / 2)

Example: 1…100
sum = (100 / 2) * 100) + (100 / 2)
sum = 50 * 100 + 50
sum = 5050

If you do the combining of the equation you only get 150.

The above uses the fact that there is a hidden number. Mainly zero(0). So it is 0+100, 1+99, etc…

99

By the way - I call this an empirical formulae because it can only be used the way it is written. Not if you do the rest of the math and condense it down to a simpler formulae.

100

The rectangular trick is by far the most intuitive