Hint: Try breaking each cog size into prime factors.

Answer: 30 revolutions.

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

63 = 3 x 3 x 7
42 = 2 x 3 x 7
35 = 5 x 7
27 = 3 x 3 x 3

We now think of rotating the large wheel just once, and this is 3 x 3 x 7 teeth moved (3 x 21), and we can see that 42 tooth wheel also has a 3 x 7 (21 teeth) in it, with an extra 2. If we therefore rotate the 63 toothed wheel twice, the 42 will have rotated three times.

The answer involves cancelling any common factors from the large wheel. We can cancel 3, 3, 7 from any of the smaller ones to leave 2 (from the 42), 5 (from the 35) and 3 (from the 27). 2 x 5 x 3 = 30. QED.

Puzzle 117

The recent BrainBashers annual marathon has just taken place. The judges have given up keeping a track of who won, as the results go missing each year. Using the following spectators' notes, can you determine who finished where?

Terry Tipton finished after Lisa Limperton and Betty Brent, but before Michael Miller.

Paul Peterson finished before David Dartford and Lisa Limperton.

Simone Stevens finished after Paul Peterson and before Jane Jacks and Helen Hall.

Kenny Kirkpatrick finished after Paul Peterson, Michael Miller and Terry Tipton.

Lisa Limperton finished after Betty Brent and David Dartford, but before Jane Jacks and Michael Miller.

Michael Miller finished after Simone Stevens and Betty Brent.

Betty Brent finished before Jane Jacks, Michael Miller and Paul Peterson.

David Dartford finished before Kenny Kirkpatrick and Terry Tipton, but after Simone Stevens.

Jane Jacks finished before Kenny Kirkpatrick, Terry Tipton and Michael Miller, but after Paul Peterson and David Dartford.

Helen Hall finished before Michael Miller but after Lisa Limperton, Jane Jacks and Terry Tipton.

ENERGY - Y = GREEN
DOORMAN - D = MAROON
CLEAREST - E = SCARLET
WEIGHT - G = WHITE
OUTLIVE - U = VIOLET
EMBARK - K = AMBER
CALMER - L = CREAM
SOLEMN - S = LEMON
VOIDING - V = INDIGO
ARCHERY - A = CHERRY

Puzzle 119

What is represented by this BrainBat?

WHEATHER

[Ref: ZKNH]

Hint: Say what you see.

Answer: Bad weather.

Puzzle 120

Using the BrainTracker grid below, how many words can you find? Each word must contain the central G 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?