I've never heard of carrot 'on' a stick. Most carrots I know would crack if put on a stick without first boring a hole in them, and then you'd have to get out a caliper and a drillset first. Sounds like too much trouble.

I guess you could 'cook' the carrot and make it soft, no no no. Then you'd have to gauge softness and if the carrot was too skinny it'd still split at the very least.

Oh, maybe you meant glue the carrot to the...........