https://radioastron.groups.et.byu.net/dokuwiki/ 2026-05-21T13:28:53-0600 https://radioastron.groups.et.byu.net/dokuwiki/ https://radioastron.groups.et.byu.net/dokuwiki/lib/tpl/byu_2017_theme/images/favicon.ico text/html 2014-07-10T19:52:27-0600 Anonymous (anonymous@undisclosed.example.com) https://radioastron.groups.et.byu.net/dokuwiki/doku.php?id=wiki:donuts:springsummer2014:answers:chess&rev=1405043547&do=diff Answer text/html 2014-07-09T12:37:01-0600 Anonymous (anonymous@undisclosed.example.com) https://radioastron.groups.et.byu.net/dokuwiki/doku.php?id=wiki:donuts:springsummer2014:answers:coins&rev=1404931021&do=diff Answer It'll take 3 rounds. Number the coins from 1-7. Beginning: H H H H H H H Round 1: flip 1, 2, 3, 4, 5 ( T T T T T H H ) Round 2: flip 2, 3, 4, 5, 6 ( T H H H H T H ) Round 3: flip 2, 3, 4, 5, 7 ( T T T T T T T ) text/html 2014-07-25T14:28:39-0600 Anonymous (anonymous@undisclosed.example.com) https://radioastron.groups.et.byu.net/dokuwiki/doku.php?id=wiki:donuts:springsummer2014:answers:cops&rev=1406320119&do=diff Answer He was walking down the street, not driving. text/html 2014-08-27T16:18:31-0600 Anonymous (anonymous@undisclosed.example.com) https://radioastron.groups.et.byu.net/dokuwiki/doku.php?id=wiki:donuts:springsummer2014:answers:dice&rev=1409177911&do=diff Answer The second die should have 3 red and 3 blue faces text/html 2014-08-15T11:35:42-0600 Anonymous (anonymous@undisclosed.example.com) https://radioastron.groups.et.byu.net/dokuwiki/doku.php?id=wiki:donuts:springsummer2014:answers:dots&rev=1408124142&do=diff Answer text/html 2014-06-19T11:45:27-0600 Anonymous (anonymous@undisclosed.example.com) https://radioastron.groups.et.byu.net/dokuwiki/doku.php?id=wiki:donuts:springsummer2014:answers:gaokao&rev=1403199927&do=diff Answer The solution to the first proof is outlined here. Given: PC is bisected by point E AC is bisected by point G Line EG bisects the two legs of triangle ACP so EG is parallel to AP EG is parallel to AP so AP is parallel to plane EDB text/html 2014-08-21T15:05:14-0600 Anonymous (anonymous@undisclosed.example.com) https://radioastron.groups.et.byu.net/dokuwiki/doku.php?id=wiki:donuts:springsummer2014:answers:jail&rev=1408655114&do=diff Answer The jailor has to make two choices: which urn does he choose from, and which disk in that urn does he choose. Lets say we leave the disks as they are. The total probability of choosing a green disk is: 1/2*(10/10) + 1/2*(0/10) = 1/2 Lets now take one green disk and put it in the other urn. text/html 2014-07-25T14:22:01-0600 Anonymous (anonymous@undisclosed.example.com) https://radioastron.groups.et.byu.net/dokuwiki/doku.php?id=wiki:donuts:springsummer2014:answers:matchtrianges&rev=1406319721&do=diff Answer By moving the bottom triangle to the side, you keep the original three triangles, while adding another smaller triangle. text/html 2014-04-30T11:07:31-0600 Anonymous (anonymous@undisclosed.example.com) https://radioastron.groups.et.byu.net/dokuwiki/doku.php?id=wiki:donuts:springsummer2014:answers:muddytracks&rev=1398877651&do=diff Answer Right to left text/html 2014-08-11T14:09:02-0600 Anonymous (anonymous@undisclosed.example.com) https://radioastron.groups.et.byu.net/dokuwiki/doku.php?id=wiki:donuts:springsummer2014:answers:oddsum&rev=1407787742&do=diff Answer 1 + 3 + 5 + ... + 97 + 99 = 2500 There are a few different tricks to this one: You use summation notation and see that it simplifies to N^2 (where N is 50) (as Richard did) You can use the Gaussian addition trick of adding pairs (1 + 99 = 100, 25 pairs so 100*25 = 2500) (Jay) text/html 2014-06-26T23:38:10-0600 Anonymous (anonymous@undisclosed.example.com) https://radioastron.groups.et.byu.net/dokuwiki/doku.php?id=wiki:donuts:springsummer2014:answers:strings&rev=1403847490&do=diff Answer The average number of crossings is 22.5. If we want to find the average number of crossings, we should model the number of crossings as a random variable. We can find the distribution and then calculate the expected value to give us our answer.