Number theory

Jine

New member
Joined
Feb 6, 2021
Messages
1
Hi need some help.
A factory uses machine to sort cards into piles. On one occasion a machine operator obtained the following curious results. When a box of cards was sorted into 7 equal groups, there were 6 cards left over; when the box cards was sorted into 5 equal groups, there were 4 left over; and when it was sorted into 3 equal groups, there 2 left. If the machine cannot sort more than 200 cards at a time, how many cards were in the box?
 
This is an instance of the Chinese Remainder Theorem, if you have learned about that.

But it is a special case that can be solved very easily by observing that in each case the remainder is 1 less than the divisor.

Ask yourself, what would happen if one more card were added to the box?
 
Top