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 Squares and Triangles (Posted on 2005-01-18)
The following sequence gives a series of square numbers,

10% of 10=1,
20% 0f 20=4,
30% of 30=9,
40% of 40=16,........
90% 0f 90=81,
100% 0f 100=100,.....

Is it possible to create a similar series that gives us triangular numbers as the result?

 No Solution Yet Submitted by Juggler Rating: 2.8000 (5 votes)

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 re: of course - Similar Result | Comment 2 of 8 |

At first I listed out the first couple triangle numbers, and then I listed out their factors. But since you are trying to find a list of numbers (List = x1, x2, x3, , xn) such that 10n% of xn = the nth triangle number, you can simply do this:

10% of x1 = 1 means x1 = 1/10% = 10
20% of x2 = 3 means x2 = 3/20% = 15
30% of x3 = 6 means x3 = 6/30% = 20
And so on.

The pattern you see is that x1=10 and xn = x(n-1) + 5 So its 10% of 10=1,
20% of 15=3,
30% of 20=6,
40% of 25=10,
50% of 30=15,
90% of 50=45,
100% of 55=55,
200% of 105=210,

So where Ady took the percents up in 5s and the numbers up in 10s, I took the percents up in 10s and the numbers up in 5s =)

Now, is someone expecting a proof that this will always be the case?  That's a little more work, I'll get back to you =)

 Posted by nikki on 2005-01-18 14:25:53

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