Reply To: The Riddle Thread….

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#1068612
Dr. Pepper
Participant

If I understand your question correctly the table would look like this:

(The charges for Plan A are rounded to the hundreth of a cent.)

Amount of Seconds 	 Plan A 	Plan B	Plan C	Plan A saved over Plan B	Plan A saved over Plan C	Plan A saved over Plan C
1 0.02 0.1 1 83% 98% 90%
2 0.03 0.1 1 67% 97% 90%
3 0.05 0.1 1 50% 95% 90%
4 0.07 0.1 1 33% 93% 90%
5 0.08 0.1 1 17% 92% 90%
6 0.10 0.1 1 0% 90% 90%
7 0.12 0.2 1 42% 88% 80%
8 0.13 0.2 1 33% 87% 80%
9 0.15 0.2 1 25% 85% 80%
10 0.17 0.2 1 17% 83% 80%
11 0.18 0.2 1 8% 82% 80%
12 0.20 0.2 1 0% 80% 80%
13 0.22 0.3 1 28% 78% 70%
14 0.23 0.3 1 22% 77% 70%
15 0.25 0.3 1 17% 75% 70%
16 0.27 0.3 1 11% 73% 70%
17 0.28 0.3 1 6% 72% 70%
18 0.30 0.3 1 0% 70% 70%
19 0.32 0.4 1 21% 68% 60%
20 0.33 0.4 1 17% 67% 60%
21 0.35 0.4 1 13% 65% 60%
22 0.37 0.4 1 8% 63% 60%
23 0.38 0.4 1 4% 62% 60%
24 0.40 0.4 1 0% 60% 60%
25 0.42 0.5 1 17% 58% 50%
26 0.43 0.5 1 13% 57% 50%
27 0.45 0.5 1 10% 55% 50%
28 0.47 0.5 1 7% 53% 50%
29 0.48 0.5 1 3% 52% 50%
30 0.50 0.5 1 0% 50% 50%
31 0.52 0.6 1 14% 48% 40%
32 0.53 0.6 1 11% 47% 40%
33 0.55 0.6 1 8% 45% 40%
34 0.57 0.6 1 6% 43% 40%
35 0.58 0.6 1 3% 42% 40%
36 0.60 0.6 1 0% 40% 40%
37 0.62 0.7 1 12% 38% 30%
38 0.63 0.7 1 10% 37% 30%
39 0.65 0.7 1 7% 35% 30%
40 0.67 0.7 1 5% 33% 30%
41 0.68 0.7 1 2% 32% 30%
42 0.70 0.7 1 0% 30% 30%
43 0.72 0.8 1 10% 28% 20%
44 0.73 0.8 1 8% 27% 20%
45 0.75 0.8 1 6% 25% 20%
46 0.77 0.8 1 4% 23% 20%
47 0.78 0.8 1 2% 22% 20%
48 0.80 0.8 1 0% 20% 20%
49 0.82 0.9 1 9% 18% 10%
50 0.83 0.9 1 7% 17% 10%
51 0.85 0.9 1 6% 15% 10%
52 0.87 0.9 1 4% 13% 10%
53 0.88 0.9 1 2% 12% 10%
54 0.90 0.9 1 0% 10% 10%
55 0.92 1 1 8% 8% 0%
56 0.93 1 1 7% 7% 0%
57 0.95 1 1 5% 5% 0%
58 0.97 1 1 3% 3% 0%
59 0.98 1 1 2% 2% 0%
60 1.00 1 1 0% 0% 0%

for the first minute.

As the amount of seconds approaches infinity the percentage of the amount saved from one plan over another tends to 0.

Take a look at the last 30 seconds of the 10th minute:

Amount of Seconds 	 Plan A 	Plan B	Plan C	Plan A saved over Plan B	Plan A saved over Plan C	Plan A saved over Plan C
5,972 99.53 99.6 100 0% 0% 0%
5,973 99.55 99.6 100 0% 0% 0%
5,974 99.57 99.6 100 0% 0% 0%
5,975 99.58 99.6 100 0% 0% 0%
5,976 99.60 99.6 100 0% 0% 0%
5,977 99.62 99.7 100 0% 0% 0%
5,978 99.63 99.7 100 0% 0% 0%
5,979 99.65 99.7 100 0% 0% 0%
5,980 99.67 99.7 100 0% 0% 0%
5,981 99.68 99.7 100 0% 0% 0%
5,982 99.70 99.7 100 0% 0% 0%
5,983 99.72 99.8 100 0% 0% 0%
5,984 99.73 99.8 100 0% 0% 0%
5,985 99.75 99.8 100 0% 0% 0%
5,986 99.77 99.8 100 0% 0% 0%
5,987 99.78 99.8 100 0% 0% 0%
5,988 99.80 99.8 100 0% 0% 0%
5,989 99.82 99.9 100 0% 0% 0%
5,990 99.83 99.9 100 0% 0% 0%
5,991 99.85 99.9 100 0% 0% 0%
5,992 99.87 99.9 100 0% 0% 0%
5,993 99.88 99.9 100 0% 0% 0%
5,994 99.90 99.9 100 0% 0% 0%
5,995 99.92 100 100 0% 0% 0%
5,996 99.93 100 100 0% 0% 0%
5,997 99.95 100 100 0% 0% 0%
5,998 99.97 100 100 0% 0% 0%
5,999 99.98 100 100 0% 0% 0%
6,000 100.0 100 100 0% 0% 0%

If there’s something I’m not understanding about your question please let me know.

(I’m not sure if I understand what you mean by “how much percent is the average billed savings”.)