Wikipedia:Reference desk/Archives/Mathematics/2021 June 15

= June 15 =

Risk board game graph
I made this diagram for the Risk (game) article. I wanted to make all edges rectilinear or at 45&deg; angles but had to use two irregular angles (between Ural and China, and between Middle East and East Africa).

Is there a way to draw the graph with all edges rectilinear or at 45&deg; angles, especially those within a continent (e.g. Ural-China)? Moving the vertex China left one space isn't a solution as Mongolia-China then becomes irregular.

Thanks, cm&#610;&#671;ee&#9094;&#964;a&#671;&#954; 00:08, 15 June 2021 (UTC)

Experiment with rotating everything surrounding Irkutsk clockwise, the see if that lets you move China left one cell. Duomillia (talk) 00:43, 15 June 2021 (UTC)

Wait, now you are in trouble China to Siberia. Never mind Duomillia (talk) 00:45, 15 June 2021 (UTC)

Ok. Try this.

Push Siam to where China is, moving Australia to the right. Push China to where Siberia is. Move all of Siberia/Japan/Mongolia up one.

Duomillia (talk) 03:25, 15 June 2021 (UTC)

Still stuck for Mongolia this time. Next, rotate Siberia/Japan/Mongolia cc by just a bit, so it forms a square instead of a diamond. Duomillia (talk) 03:32, 15 June 2021 (UTC)

As for Middle East to East Africa, do you permit your routes to cross over each other? I suspect that's the only way to accomplish part 2. Do South Africa > Madagascar > East Africa > Egypt > right Duomillia (talk) 04:27, 15 June 2021 (UTC)

I found a way to make the other connection work: --116.86.4.41 (talk) 08:47, 15 June 2021 (UTC)

Also, the above solution for Ural–China forces the Alaska–Kamchatka link to break the alignment. An alternative solution for Ural–China without that problem is: move 6,5,12,4,8,10,2 up one space; move 1 and 3 to the right one space; and move 9 up and to the right one space; then move Australia over (several positions work), and move North America up one space to re-align the Alaska–Kamchatka link. --116.86.4.41 (talk) 08:59, 15 June 2021 (UTC)


 * Thank you very much, and user at 116.86.4.41. I've adopted Duomillia solution (with Japan moved right to avoid overlapping edges). Though 116.86.4.41's solutions satisfy my criteria, they make the graph one or more columns wider. As I already had trouble with text being too small, I decided that having irregular intercontinental routes as drawn is an acceptable compromise. Thanks again, cm&#610;&#671;ee&#9094;&#964;a&#671;&#954; 11:58, 15 June 2021 (UTC)


 * My alternative solution for Ural–China can fit in the same amount of space as your current diagram if Australia is rotated clockwise:

--116.86.4.41 (talk) 08:17, 16 June 2021 (UTC)
 * Many thanks, that fixes the Alaska-Kamchatka link, though having Australia rotated is too big a compromise in my opinion. cm&#610;&#671;ee&#9094;&#964;a&#671;&#954; 11:06, 16 June 2021 (UTC)
 * P.S. Compact layout (but with Kamchatka on the right) found &rarr;
 * I realised that if all diagonals in a row or column of a continent are parallel, the entire row or column can be translated one space, such as what I've done with the columns of North America. The graph is now just 10 columns wide and 7 rows high, and the continents are roughly the correct shape. Cheers, cm&#610;&#671;ee&#9094;&#964;a&#671;&#954; 01:06, 17 June 2021 (UTC)

Investment appraisal
A dealer bought a car for#1440000. At what price must he sell it in order to make a profit of 20% on the selling price?


 * Give you a hint? If he needed to make 100% profit he would need to charge 2.0 times, and if he needed to make 50% he’d sell for 1.5 times. Duomillia (talk) 17:54, 15 June 2021 (UTC)


 * ..., assuming that the profit percentage is in terms of the buying price (₦1440000). I would have formulated the question as just: "At what price must he sell it in order to make a profit of 20%?" The profit is the difference between the selling price and the buying price; in an equation: profit = (selling price) − (buying price). So then (selling price) = (buying price) + profit = (buying price) + (20% of buying price). See also our article Percentage. --Lambiam 21:33, 15 June 2021 (UTC)