Question 45
Carlos writes on the board, from left to right, the 20 integers from $1$ to $20$ in some order. Then, under the first number written, write the product of the first and the second; Under the second number write the product of the second with the third and so on, under the second to last write the product of the second to last with the last. Thus obtaining a new list with $19$ integers.
It does this process repeatedly with the new numbers obtained, so that on each line the number of numbers is reduced by one; Finally, on the last line, Carlos writes only a number.
Show an initial ordering of the $20$ numbers so that the last number Carlos writes is the smallest possible. How many of these arrangements are there?
It does this process repeatedly with the new numbers obtained, so that on each line the number of numbers is reduced by one; Finally, on the last line, Carlos writes only a number.
Show an initial ordering of the $20$ numbers so that the last number Carlos writes is the smallest possible. How many of these arrangements are there?