Brian the engineer disassembles an old Warcom press brake, and begins playing with the gears he finds inside it. He has 3 cogs: A, B, and C. All of which have at least 8 teeth, and no cog has more than 40 teeth. Cog B is the biggest and has the same number of teeth as cogs A and C added together. Brian arranges the cogs as shown below. A red dot is drawn at the top of each of the cogs, and cog A has a crank handle attached to it, also shown in the diagram. As the crank handle is turned, Brian notices the dots rotate out of their positions at different speeds. He continues to turn the crank handle in the same direction until all three of the dots simultaneously appear back in the positions they started in, and then stops turning. Brian reports that during the turning, cog C made 45 revolutions more than cog A. How many teeth do each of the cogs have? Answers via PM.
I haven't started yet, but I think I know where this puzzle is going... When's the closing date, Jadzia? I think I'll get working on it tomorrow.
back I'd better get my thinking cap on, then. I'm guessing that when Brian () turns the first cog, at no time during the turning are the dots back in their original alignment until he stops at the end. That makes it more interesting...
Yes, that is implied in the wording of the question. Otherwise there would be many solutions, like various multiples of 2:3:1. And Zyon offers the first correct answer.
If you can work out the correct trajectory, angle of fire, force of thrust required, and probability of success... then go for it.
I thought it would make a nice change to counting the vowels in a set of place names Is nobody but Zion and RJ going to make a guess??
This explains why the Warcom was inoperative this morning... And this gear ratio stuff is too much like work I tell you!
*nails sign to press-brake* ACHTUNG! ALLES TURISTEN UND NONTEKNISCHEN LOOKENPEEPERS! DAS BENDINGSCHNITCLE IST NICHT FÜR DER GEFINGERPOKEN UND MITTENGRABEN! ODERWISE IST EASY TO SCHNAPPEN DER SPRINGENWERK, BLOWENFUSEN UND POPPENCORKEN MIT SPITZENSPARKSEN. IST NICHT FÜR GEWERKEN BEI DUMMKOPFEN! DER RUBBERNECKEN SIGHTSEEREN KEEPEN DAS COTTONPICKEN HÄNDER IN DAS POCKETS MUSS. ZO RELAXEN UND WATSCHEN DER BLINKENLICHTEN.