Dérailleur de Rigueur

Quand le dérailleur est de rigueur?
-- Brigitte Niquette
lthough it may be somewhat difficult to make out in the photograph on the left, Brigitte's mountain bike is configured with conventional gearing as depicted in the sketch on the right.

Look closely and you will see that the...

• 'Crankset' has three sprockets, each one selectable by the 'front dérailleur' and the...
• 'Freewheel' has seven sprockets, each one selectable by the 'rear dérailleur'.
Look closer still and you will be able to count the 'teeth' on each sprocket...
• Crankset: 28, 38, 48, and...
• Freewheel:  13, 15, 18, 19, 21, 24, 34
It is customary to provide an 'index' for each dérailleur to denote the present position of the 'chain'...
• Front dérailleur: #1~28, #2~38, #3~48, and...
• Rear dérailleur: #1~34, #2~24, #3~21, #4~19, #5~18, #6~15, #7~13
The puzzle entitiled "Inches per What?" provides the rationale for measuring the 'speed' of a bicycle in 'inches' along with how to perform the requisite calculations.

 How many 'speeds' are determined by the dérailleurs on Brigitte's mountain bike?
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