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This would break if there are file names with spaces and/or special characters. To avoid that you would need to use properly quoting:
print "$FILE"
tail -1 "$FILE"

Also, wc -c only counts bytes,...

Try:
find sent/ -type f -exec tail -1 {} \; | awk '{print length}'
To also count the linefeed at the end of the line, like wc -c or wc -m use awk '{print length+1}'



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Use wc -c counts...