The other day I met an old college friend in a coffee shop. We both were students in the Math department of that college. Here was our conversation (after the small talk)
We are meeting first time after college! She said
Yes. What is it, 25-30 years?
Yup. Just celebrated my __th Birthday.
Wow. That is a milestone.
Everything downhill from here!
So how many kids do you have?
How old are they?
You will have to guess that, Mr. Math from my college.
So on my Birthday, I gave them some gold and silver coins. I had same number of gold and silver coins each. Same number (each) as my age.
So number of gold coins equals number of silver coins equals your age?
Right. This is how I distributed the Gold coins. Each kid got same number of gold coins as their age number. I used up all the gold coins that way.
How about the silver coins?
I did it differently. Each kid got silver coins equal to the next higher age number of their sibling. Used up all silver coins also. Can you guess their ages?
Higher age number of just one sibling?
No I need more info.
Two kids got same total number of coins each. The other two kids also got same total number of coins each but this number was different than what the other 2 got. Can you guess?
No. I need more.
No. I think you just need a paper and pencil. Give me a call when you solve it. I gotta go.
You in a rush?
Yup. Kids are home. The teenager needs a ride.
After a few minutes it hit me. I knew their ages and how many coins each kid received. Do you? Can you do it with just paper and pencil?