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Hint: Try breaking each cog size into prime factors.

Answer: 140 revolutions.

If we break each wheel into its prime factors, we get:

168= 2 x 2 x 2 x 3 x 7
49 = 7 x 7
32 = 2 x 2 x 2 x 2 x 2
15 = 3 x 5

So

revolutions x 168
---------------------------------
2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7

revolutions x 2 x 2 x 2 x 3 x 7
---------------------------------
2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7

revolutions
-------------
2 x 2 x 5 x 7

revolutions
-------------
140

Which means revolutions = 140. QED.

Puzzle 387

Starting with the 6 in the bottom left corner, what is the highest total you can make, if you only move up or right, using the mathematical signs on the way?

Hint: There is only one way to make the middle 25.

Answer:

Puzzle 390

Using the BrainTracker grid below, how many words can you find? Each word must contain the central K and no letter can be used twice, however, the letters do not have to be connected. Proper nouns are not allowed, however, plurals are. Can you find the nine letter word?