Question 30
Optional bonus question. A paper strip has cells labeled 1 to 10. Follow these steps:
1. Choose one number from 2, 3, 4, 5, 6, 7, 8 or 9.
2. Cut out its cell so that the strip separates into a left piece and a right piece.
3. Multiply all the numbers on each piece, excluding the chosen number. You obtain a left product and a right product.
For example, Manee chooses 5 and cuts its cell. Her left product is $1\times2\times3\times4=24$; her right product is $6\times7\times8\times9\times10=30240$.
Mana follows the same steps and gets equal left and right products. Which number did he choose?
1. Choose one number from 2, 3, 4, 5, 6, 7, 8 or 9.
2. Cut out its cell so that the strip separates into a left piece and a right piece.
3. Multiply all the numbers on each piece, excluding the chosen number. You obtain a left product and a right product.
For example, Manee chooses 5 and cuts its cell. Her left product is $1\times2\times3\times4=24$; her right product is $6\times7\times8\times9\times10=30240$.
Mana follows the same steps and gets equal left and right products. Which number did he choose?