Thank you for replying, Scott. However, I don’t understand 1:30/7:30 designation as the countable corners are onlybat the stops of the minute hand and at these times the minute hand is not at a stop.
Summary: interesting counting problem for fun
Imagine we draw a circle with diameter d and mark off sixty equal intervals like minutes on a clock. Then we draw two diameters perpendicular to one another and divide each in sixty equal intervals. Using the intervals on the diagonals we lay out a...
I think that the general formula would take this form;
$$m+1 {n \choose 2} + m-1 \sum_{i=2}^{n-1} m^{i-1} {n-i+1 \choose 2}$$
where m is the number of spaces in the matrix and i the number of rows
the calculation for 6 rows where m =10 and i=6
For 6 rows
11 x 6C2 + 9(10 x 5C2 + 100 x 4C2...
11 x nC2 + 9∑i=2n-1 10i-1 x (n-i + 1)C2
Here is the formula using the formatting the best I could. I have included a calculation of a 10 space grid of 11 dots with 5 rows.
11 x 5C2 + 9 ∑4i=2 104-1 x (5-2 + 1)C2
simplifying
110 + 9(10 x 4c2 + 102 x 3C2 + 103 x 2C2)
simplifying
110 + 9(60...
another try at math formatting. anyone who can correct i would be most gratified.
11 x nC2 + 9∑10i-1 x (n-i +1)C2
beneath the sigma i=2 above the sigma n-1
I worked out the answer with a mathematician earlier today. I will try to post it using math symbols the best I can.
n-1
11 x nC2 + 9Σ 10superscript i-1 x (n-i + 1)C2
i=2
Please review this to see if it agrees with your answer. I will put up some...
The above description was composed by my friend who is a Phd in math. He said it might be easier to understand for a mathematician. We disagreed on the meaning of "coincision" which I outlined in the original problem but I yielded to him. It is an extremely difficult problem but I am hoping it...
Call the Array of nodes (points) A. A has dimension n rows by m columns, where m depends on n. The following explains the concept for n=3; The first row of A has nodes A(1,1) ... A(1,11) The second row of A can be labeled A(2,1) . . . A(2,101). The third row can be labeled A(3,1) ... A(3,1001)...
I have a diagram but I don't know how to post it. Okay look below. Row 1 has the original ten spaces i referred to. The first column in this diagram has 2 dots one from row 1 and 1 from row two. That represents one coincision. Row 2 will have the dots all the way across dividing each of the...
Imagine we take a sheet of paper and along the bottom lay out ten equal spaces by marking off 11 equally placed points. We label this row 1. Directly above these points we mark off another 11 points to correspond to our first eleven points only this time we divide the ten spaces of this row into...
A set with zero elements, or a set with an infinite number of elements of zero magnitude can exist in only one place, and that is the imagination. If you use a mathematical construct that exists in the imagination, as ideas let us say, and that construct proves to have a valid application in the...
Did you express similar doubts to your teacher at the time :p:p:p:p:p:p:p:p Bill, I shall ignore this rather gratuitous remark. But are the points of space little three dimensional balls? two dimension circles? are there an infinite number of whatever they are? a finite number? can space curve...
Thank you so much for responding. However, I can't get past the statement, "everywhere in space." It makes absolutely no sense, logically or mathematically. You can describe space in all kinds of ways, in many different systems, but you cannot account for a field as just a set of points. I'm...
I read in an article that a quantum field is one where every point in the field is defined by an imaginary number. If you square the imaginary number you get a wave function. But can a three dimensional field be defined by a set of points, finite or infinite? Does it mean a field characterized...