2 answers to the riddle

DAF HASHAVUA
MAKOS 22a

 A  שליח בית דין who gave 40 lashes, according to 
the תנא קמא he was עובר on the לאו of ולא יסיף and 
according to ר' יהודה, he did the proper מצות מלקות.

If this  שליח בית דין was עובר another 39 לאוין  then,

According to the תנא קמא, he was עובר in total 40 לאוין
40X39 = 1560

According to  ר' יהודה, he was עובר in total 39 לאוין
39X40 = 1560

According to both, the תנא קמא and ר' יהודה, he will
end up with 1560 lashes, 

The answer above was given by the חידושי הרי"ם as a child.


Another answer   ( source- unknown )

שליח בית דין who gave 79 lashes to someone 
who is חייב מלקות  (a single set)

According to the תנא קמא, he was מוסיף* 
40 lashes
40X39 =1560

According to ר' יהודה he was מוסיף*
39 lashes
39X40 =1560

* In such  conditions where he would be חייב for each lash






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