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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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 Investigation Of The Second Form | Comment 7 of 8 |
(In reply to Investigation Of The First Form by K Sengupta)

We consider the form (a, b) = (n+1)r, nt), with rt = 50

Since r and t are positive integers, it follows that:
(r, t) = (1,50); (2, 25); (5, 10); (10, 5); (25, 2); (50, 1)

The last value of (r,t), that is (50, 1), can be ignored as we would reach 100% at the very second step.

Now, (r,t) = (1,50) gives: (a, b) = (n, 50(n+1)) yielding Series (vi)
(r,t) = (2,25) gives: (a, b) = (2(n+1), 25n) yielding Series (vii
(r,t) = (5,10) gives: (a, b) = (5(n+1), 10n) yielding Series (viii)
(r,t) = (10,5) gives: (a, b) = (10(n+1), 5n) yielding Series (ix)
(r,t) = (25,2) gives: (a, b) = (25(n+1), 2n) yielding Series (x)

The Series (vi) to (x) are displayed hereunder as follows:

Series(vi)

2% of 50 = 1
3% of 100 = 3
4% of 150 = 6
5% of 200 = 10
6% of 250 = 15, and so on
.............
.............

Series (vii)

4% of 25 = 1
6% of 50 = 3
8% of 75 = 6
10% of 100 = 10, and so on
..............
..............

Series (viii)

10% of 10 = 1
15% of 20 = 3
20% of 30 = 6
25% of 40 = 10, and so on
.............
.............

Series (ix)

20% of 5 = 1
30% of 10 = 3
40% of 15 = 6
50% of 20 = 10
60% of 25 = 15, and so on
................
................

Series (x)

50% of 2 = 1
75% of 4 = 3
100% of 8 = 6
(Since by the problem, the series concludes as soon 100 percent
is reached)

 Posted by K Sengupta on 2007-06-28 11:22:15

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