Pyr­gic puz­zles

The Guardian - Journal - - Puzzles -

Pedan­ti­cus was in a fine mood and things were go­ing along trip­pingly. Then the word “heartwrench­ing” is­sued forth from his lit­tle DAB ra­dio and he made a clutch for his heart. What had thrown a span­ner into the works? Garabag­gio’s Lady­bug on an Igloo cur­rently on dis­play at the Rogue’s Gallery on Pop­py­cock Ter­race shows a dot on the arc of a semi­cir­cle. Why, a child could have pro­duced it! To soothe my out­rage at what passes for art in this cor­rupt world of nin­nies I con­soled my­self with a huge slice of car­rot cake from the café and the thought that it could at least be turned into a ge­om­e­try puz­zle. For Art’s loss has so of­ten proved Ge­om­e­try’s gain. I mea­sured the lengths shown (the se­cu­rity is lax — who would bother to steal this stuff ?); so if P rep­re­sents the la­dy­bird and it started an hour ago at A and be­gan to walk (uni­formly as ge­o­met­ri­cal la­dy­birds do in puz­zles) around the arc, when will we look to it to ar­rive at B? How high is the la­dy­bird presently above the line AB? How far is it from A? And how far from B? Down at the Last Chance sa­loon Sher­iff Ein­stein’s cuckoo clock is work­ing. One bird (the black one) ap­pears at in­ter­vals of ex­actly one hour, the other (the white one) ap­pears at in­ter­vals of ex­actly ev­ery two hours, but each bird started at a ran­dom time in­de­pen­dently of the other. Gullible Gus walks into the sa­loon. What are the chances the first bird that pops out of the clock will be the black one?

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