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Squares and Triangles (Posted on 2005-01-18) Difficulty: 2 of 5
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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Solution Investigation Of The First Form | Comment 6 of 8 |
(In reply to Generalised Parametric Solution by K Sengupta)

We consider the form (a, b) = (nr, (n+1)t), 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 (i)
(r,t) = (2,25) gives: (a, b) = (2n, 25(n+1)) yielding Series (ii)
(r,t) = (5,10) gives: (a, b) = (5n, 10(n+1)) yielding Series (iii)
(r,t) = (10,5) gives: (a, b) = (10n, 5(n+1)) yielding Series (iv)
(r,t) = (25,2) gives: (a, b) = (25n, 2(n+1)) yielding Series (v)

The Series (I) to (v) are displayed hereunder as follows:

Series(i)

1% of 100 = 1
2% of 150 = 3
3% of 200 = 6
4% of 250 = 10
5% of 300 = 15, and so on
.............
.............

Series (ii)

2% of 50 = 1
4% of 75 = 3
6% of 100 = 6
8% of 125 = 10
10% of 150 = 15, and so on
..............
..............

Series (iii)

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

Series (iv)

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

Series (v)

25% of 4 = 1
50% of 6 = 3
75% of 8 = 6
100% of 10 = 10
(Since by the problem, the series concludes as soon 100 percent is reached)


  Posted by K Sengupta on 2007-06-28 11:20:17
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