Calcudoku.org 20 Million Solved Puzzles Analysis

Hi, guys. Everybody on calcudoku.org is eagerly anticipating the moment puzzle number 20 million is solved. Given my investigative nature and affinity for math and science, I’ve done an experiment to estimate when that spectacular moment will occur. I've printscreened and recorded the total number of solved puzzles at 18:00 USA/Canada EST/EDT for 10 days. Day 1 is Monday, October 21, 2019 and will be x = 0 on a Cartesian coordinate plot. I found the number of puzzles solved on each of the ten days, took an average of those ten days and used a trendline. Last but not least, I compared the trendline equation with my 10 day average to estimate when number 20 million will arrive.

First, here's a summary of my data.

The left to go readings were calculated by subtracting a given day's 18:00 reading away from 20 million. I found the puzzles solved on a given day by subtracting that day's 18:00 reading from the next day's 18:00 reading.

In other words,

Day 1 puzzles solved = Day 2 18:00 reading - Day 1 18:00 reading or

19,135,658 - 19,127,738 = 7,920 puzzles solved on Day 1.

I took an 18:00 reading on Day 11 because I needed it compute the puzzles solved on Day 10.

To estimate when the puzzles left to go will equal 0, I decided to compute the slope of a trendline after each day of my analysis. I couldn't do that on Day 1 since 2 points are needed. You may remember from algebra that slope is equal to the change in y over the change in x (colloquially referred to as "rise over run"). Furthermore, a linear equation is written in slope-intercept form as

y = mx + b where m is the slope and b is the y-intercept of the line (where x is 0).

In my experiment, the y-intercept is 872,262.

I used the following to obtain the slope for Days 1 and 2:

(0, 872,262) and (1, 864,342)

x1 y1 x2 y2

or m = (864,342 - 872,262)/(1-0) = -7920

Therefore, the equation of the line for Days 1 and 2 is y = -7,920x + 872,262.

To find the trendline for Day 3, I plotted the x values for the first 3 days against the left to go values for those days in Microsoft Excel. I displayed the equation and R^2 value on the chart, and I set the intercept to 872,262. In doing so, the equation I got was:

y = -8,404.8x +872,262 with an R^2 value of 0.998.

I repeated this process each day for all 10 days, obtaining a final trendline of

y = -8,178x + 872,262 and an R^2 value of 0.9982.

I looked at the slopes of my trendlines, obtaining an average slope of -8,108.3. Additionally, the average number of puzzles solved per day worked out to 8,314, which is fairly close to 8,108. Those trendlines were set equal to 0 and solved for x, the number of days it would take for the left to go number to equal 0. I rounded my x numbers to 3 decimal places, and I figured out the hours, minutes, and seconds as well. From my calculations, I estimate that puzzle number 20 million will be solved somewhere in the time ranges shown below.

US/Canada Eastern Time: between Sunday, February 2, 2020 at 12:45 to Saturday, February 8, 2020 at 22:41Central European Time (CET)/Patrick's Time: between Sunday, February 2, 2020 at 17:45 to Sunday, February 9, 2020 at 03:41 Last but not least, I wanted to include screenshots of the 18:00 readings I took for each day. I'll fix this post up later if my pictures didn't show up.

skeeter84

P.S. Now that I think about it, I'll go back on imgur to resize my stuff.