how many distinct values does it have? I solved this problem by manually adding parentheses and counting them, and got correct answer of 32. Is there a simple to find the answer? Thanks.

The value of the expression $1÷2÷3÷5÷7÷11÷13$ can be altered by including parentheses. If we are allowed to place as many parentheses as we want, how many distinct values can be obtained for this expression?


adding parenthesis changes the answer at all points but the end point due to the orders of operation. we have 6 divisions and one doesn't count so 5. each parentheses can either be included or not included so 2 options. in the end we have $2^5=32$
