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or is there a cheaper option based upon 10-speed cassettes and a spacer?
If you have 11-speed shifters, you're stuck with 11-speed cassette spacing. Oddly, Shimano have abandoned junior gearing for 11-speed, they always used to make Ultegra cassettes with big sprockets at the top end.
16-17-18-19-20-21-22-25-28-32
I think that could be assembled from an 11-28 and an 11-32, you'd need a spacer between the lock ring and the 16T to take up the slack. With some frames, you may crash the chain into the seat stay by using such a large sprocket. It's probably easier just to leave things as they are.
The other option is a 1×11 set up - 36/11 gives a development of fractionally under 6.93m with 700×23C tyres.
gbj_tester
@mespilus
British Cycling Tech. Reg. 3.3 gearing for younger riders.
mespilus jr. spent this morning, his second, at the Hillingdon Track,
gaining his Bronze accreditation,
and being allowed into a 5 lap race with far more experienced
members of Hillingdon Slipstreamers.
As a 14 yo he is restricted to a gear of 6.93m,
meaning that the bottom five gears are currently locked off.
(His mother panicked and ran out and bought him a bike
off the peg with an 11-speed Dura Ace groupset).
His current smallest sprocket is 16-toothed.
Is it possible to mix'n'match some combination of CS5800 105 cassettes
to give him a 16-17-18-19-20-21-22-25-28-32-?
or is there a cheaper option based upon 10-speed cassettes and a spacer?