[X]

Privacy Policy + T&C

We use cookies to personalise our content and ads, and for traffic analysis. Information about your use of our site is shared with our advertising and analytics providers. You also agree to our T&C.

[X]

Common Answers

Have you entered September's Common Answers?

BB Logo Spacer
Spacer
Line
Line

Puzzle - Answer

I have a machine which has four sequential cog wheels in constant mesh.

The largest cog has 102 teeth and the others have 60, 46 and 34 respectively.

How many revolutions must the largest cog make before each of the cogs is back in its starting position?

?

 [Ref: ZPLO] © Kevin Stone

Answer: 230 revolutions.

We are after a number such that (revolutions * largest cog) / (every small cog) is an integer. This is easily achieved by looking at the cogs' prime factors:

102 = 2 * 3 * 17
60  = 2 * 2 * 3 * 5
46  = 2 * 23
34  = 2 * 17

So

   revolutions * 102
-----------------------
2 * 2 * 3 * 5 * 23 * 17

  revolutions * 2 * 3 * 17
= ------------------------
  2 * 2 * 3 * 5 * 23 * 17

  revolutions
= -----------
  2 * 5 * 23

Which means revolutions = 230. QED

Back to the puzzles...

 

 



This website uses cookies, for more information please view our privacy policy. By using the site you also agree to our terms and conditions.

Line
Line