The simplest thing to do would be to count the campers the way we count 10 men for a minyan, by saying the pasuk "hoshiya es amecha..." which has 10 words and each camper will be one word. You can repeat the pasuk until you have covered everyone. Even if you don't have a multiple of 10 in your group, you can count the remaining words to get an accurate count. For example, if you have 24 campers you would expect to finish the pasuk twice and get up to the word "uvareich" the third time.
If this is not practical, you can count caps or backpacks instead of people, as we find when the Jewish People were in the desert they each gave a half-shekel coin to be counted even though each coin represented a person. The only issue is with counting directly.
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