{"id":4266,"date":"2025-02-15T09:16:32","date_gmt":"2025-02-15T14:16:32","guid":{"rendered":"https:\/\/josmfs.net\/?p=4266"},"modified":"2025-03-01T09:14:47","modified_gmt":"2025-03-01T14:14:47","slug":"cat-and-mouse","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2025\/02\/15\/cat-and-mouse\/","title":{"rendered":"Cat and Mice"},"content":{"rendered":"

\"\"This is a classic puzzle from Boris Kordemsky\u2019s 1972 Moscow Puzzles<\/em>.<\/p>\n

\u201cPurrer has decided to take a nap.\u00a0 He dreams he is encircled by 13 mice: 12 gray and 1 white.\u00a0 He hears his owner saying: \u201cPurrer, you are to eat each thirteenth mouse, keeping the same direction.\u00a0 The last mouse you eat must be the white one.\u201d\u00a0 Which mouse should he start from [eat first]?\u201d<\/p>\n

Answer<\/a>.<\/p>\n

See Cat and Mice<\/a> for a solution.<\/p>\n

The Josephus Problem<\/strong><\/span><\/p>\n

\"\"<\/a>This famous Josephus Problem<\/a> presented on Youtube is somewhat different from the Cat and Mice puzzle, but still has similarities.\u00a0 An article<\/a> by Jay Bennett discussing the problem was published in Popular Mechanics in 2016.<\/p>\n

 <\/p>\n

Penn and Teller \u2013 Spelling Cards<\/strong><\/span><\/p>\n

\"\"<\/a>It turns out that Penn and Teller have performed another magic trick recently that is based on mathematical principles and so is more or less self-working.\u00a0 It is a more complicated version of the Cat and Mice puzzle, which I have dubbed the \u201cSpelling Cards\u201d trick. <\/p>\n

What follows is a detailed narration of the trick.\u00a0 But it is easier and more fun to watch the video<\/a>.<\/p>\n

Characters Piff, Pop (Penn), and Squire (Teller), along with Brook carry out the trick.\u00a0 Piff shows 10 cards and then holding them face down asks Brook to name the most important card, and she says an ace.\u00a0 So Piff begins counting 3 cards for each letter in the name of the card.\u00a0 As he removes each face-down card from the top of the pack, he puts it on the bottom.\u00a0 After placing the third face-down card on the bottom, he turns the next card face up and shows it to be the ace of clubs.\u00a0 He tosses it away.<\/p>\n

Next Penn takes the pack and counts off 3 cards for \u201cdos\u201d (two) and turns over the next card on top.\u00a0 It is a two of hearts, which he then tosses away.\u00a0 Now it is Teller\u2019s turn and he counts off 5 cards for \u201cthree\u201d and shows a three of spades.\u00a0 He tosses that away.\u00a0 Finally Brook takes the pack and counts off 4 cards for \u201cfour\u201d and turns over the next card.\u00a0 But it is the ten of diamonds!\u00a0 Oops.\u00a0 So Brook puts the ten back on the pack and hands it to Piff.<\/p>\n

Piff again counts 4 cards and turns over the next revealing the four of clubs, which gets tossed.\u00a0 Penn counts off 4 cards for \u201cfive\u201d and turns over the 5 of hearts, and that gets tossed.\u00a0 Brook counts off 3 cards for \u201csix\u201d, but again turns over the ten of diamonds.\u00a0 She puts it back on the stack, and Teller has a go.\u00a0 He counts off 3 cards again and turns over the six of hearts, which he tosses.<\/p>\n

Brook tries again and counts off 5 cards for \u201cseven\u201d, but again turns up the ten of diamonds.\u00a0 Returning the ten to the pack she gives it to Piff, who counts of 5 cards again and turns over the seven of spades.\u00a0 Piff tosses the card.\u00a0 Brook tries once more by counting off 5 cards for \u201ceight\u201d, but again turns over the ten of diamonds.\u00a0 Teller has a go and counting off 5 cards arrives at the eight of clubs, which he tosses.\u00a0 Frustrated Brook tries a final time and counts off 4 cards for \u201cnine\u201d.\u00a0 And of course she turns over the ten of diamonds again.\u00a0 Teller again takes the pack (watch the video carefully here) and counts the four cards turning over the nine of hearts, which he tosses.\u00a0 With only one card left, Teller gives it to Brook to \u201ccount\u201d the card 3 times for \u201cten\u201d to reveal again the ten of diamonds, but this time appropriately.<\/p>\n

So the question is, what is the initial arrangement of the cards so that this trick will work automatically?<\/em><\/p>\n

Answer<\/a>.<\/p>\n

See the Spelling Cards<\/a> trick for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"

This is a classic puzzle from Boris Kordemsky\u2019s 1972 Moscow Puzzles. \u201cPurrer has decided to take a nap.\u00a0 He dreams he is encircled by 13 mice: 12 gray and 1 white.\u00a0 He hears his owner saying: \u201cPurrer, you are to eat each thirteenth mouse, keeping the same direction.\u00a0 The last mouse you eat must be […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[90,281,279,280,278],"class_list":["post-4266","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-binary-numbers","tag-josephus-problem","tag-magic","tag-moscow-puzzles","tag-penn-and-teller"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4266","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=4266"}],"version-history":[{"count":4,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4266\/revisions"}],"predecessor-version":[{"id":4308,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4266\/revisions\/4308"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=4266"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=4266"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=4266"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}