"On their back" or "on their backs"?

Solution 1:

Plural, because we are, in fact, dealing with eight little backs. And a back is a back, no matter how small. A child has a back, but children have backs.

I'm sure others will back me on this.

Solution 2:

The semantic, grammatical, and logical arguments clearly suggest it's 'correct' to use the plural, and that's what most people do.

However, despite the fact that I doubt if any style guide endorses the singular, it seems that about 10% of usages for back persist in using the singular.

For reasons which escape me, that 'incorrect' minority rises to nearly 25% when the body part in question is chest. In both cases the evidence strongly suggests the incorrect usage is becoming more widespread.

Personally I believe it's a situation where grammarians backed the wrong horse, and their blind prescriptivism will eventually be defeated. People quite naturally want to use the singular when the number of [body parts, whatever] is immaterial, and only the plurality of [babies, people] is relevant. Increasingly, it seems, they're prepared to do this even at the risk of being considered illiterate.