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Across: DUCK, PLUM, TOES, BALE
Down : DOME, PLUS, CUBE, TALK
Boxes : DUMP, LUCK, SOLE, BEAT
Note : Other anagrams of these words are OK as long as they don't change the answer grid.
Puzzle 403
I have a machine which has four sequential cog wheels in constant mesh.
The largest cog has 168 teeth and the others have 49, 32 and 15 respectively.
How many revolutions must the largest cog make before each of the cogs is back in its starting position?
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 404
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?
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