A child has fewer than 200 baseball cards. If he puts them in piles of 3, 5, 6, 8, or 12 he has one card left over each time. How many baseball cards does he have?

Answer 1

Linh, since you’ve called this an elementary math problem I’ll assume you don’t have access to algebra. But you are familiar with number lines. So you can solve this problem using a “sieve”.

First, draw a long number, starting at 0, and a mark at every number up to 200. That’s tedious, I know.

Next, we will identify all the numbers that could be right answers for piles of 3. What will that look like?

The problem says the kid made piles of 3, and had 1 left over. So, take a pile of 3 in one hand, and imagine dealing them out one at a time. So, put your finger on number 0, count 3, and then move over 1. Where are you? You’re at 4, put a check mark above number 4. Now count 3, and put a check mark above that number, 7. Keep going, putting a mark after every 3. That will be marks at numbers 4, 7, 19, 13, etc.

Now do the same with 5’s. Put your finger on 0, count 5, move over 1. Where are you? At 6, put a mark. Count 5, put a mark at 11, 16, 21, etc.

Now do the same with 6: start at 0, count 6, move over 1 and put a check mark at 7, 13, 19, 25, 31, etc.

Now do the same with 8: start at 0, count 8, move over 1 and put a check mark at 9, 17, 25, 33, 42, etc

Now do the same with 12: start at 0, count 12, move over 1 and put a mark at 13, 25, 37, 49, etc

Finally, how do we find an answer? We want a number that has all 5 check marks. For example, the number 13 has how many check marks? It has 3 check marks. Move to the right looking for the first number with 5 check marks. That number passed through all 5 sieves. It’s your answer.