Question

Dear Mitch,

I don't even know if this will get to you in time to read it, but if you do tomorrow's father's day and I just remembered that when I asked my dad what he wanted for father's day, he said one thing he would really love is if I gave him a bunch of brain-twisters and weird math problems. I know there's a lot of books on them, but I don't drive and can't order anything by tomorrow. And on top of it all, he said the really best type I could give him would be ones I made up myself!!!???!!

I know he wants me to come to like those things like he does, but making them up myself...I DON'T THINK SO!

But then I thought if you could give me a couple and maybe give me a hint or two on how to make them up, then at least I can try. I can stay up late, my parents really don't mind on the weekends and so I'll check every hour or so to see if you got to my letter. Even if you don't though, that's cool, and maybe next year.

Sincerely,

Michael E.

Bangor, Maine

Answer

Dear Michael,

Your Dad sounds cool.

I'll give you a few and then try to show you a pattern you might be able to use to make up your own... it's not that hard!

- Joe's father is twice as old as Joe. Together their ages add up to 90. How old is Joe?
- Mike's father is twice as old as Mike. Together their ages add up to 75. How old was Mike six years ago?
- Leroy's father is twice as old as Leroy. Together their ages add up to 84. What did their ages add up to six years ago?
- Benum-la-forte Vinya-Runyen's father will be twice as old as Benum-la-forte Vinya-Runyen five years from now. Right now their ages add up to 92. How old will Benum-la-forte Vina-Runyen be when his father is twice Benum-la-forte's age?
- Coolunim B. Roolunim's father will be twice the age of Coolunim B. Roolunim six years from now. The sum of their ages at that time will be a number that is a 3-digit number that has no zeros in any of its digit-places, ends with a one, and is divisible by 3. Right now their ages add up to a number that is a multiple of 3 and a multiple of 9 (but has other factors as well). By the way, right now Coolunim is younger than forty, older than thirty, and (right now) is a prime number. How old will Coolunim B. Roolunim be twelve years from now?

And how old was his father 15 years ago?

**FINALLY:**

Susan's age and her father's age add up to 66. If her father is 24 years older than Susan, how old is Susan's father's father (Susan's Grandfather) if he is four times as old as Susan?

Now, those ought to keep your father engaged for at least a little while. You can either write them out or type them up or just print them out.

I will reveal all the answers and how to arrive at them by early tomorrow evening.

One simple pattern is taking a number that is divisible by 3. Make it big enough so the question makes reasonable sense (you don't want the answer to be that someone's grandfather is five years old! (And you probably should stay away from a number that is so large that one of the characters ends up being two hundred years old.)

So it's not a bad idea for this step to choose a number between 60 and 150.

After you have your number that is divisible by three, divide it by three.

That will give you a quotient. (Which is just a fancy word for the answer of a division problem).

The quotient is the son's age. Write that down somewhere so you don't forget. Then multiply that quotient by two and you will get the father's age for a problem in this format:

Hank's Dad is twice the age of Hank. Together, their ages add up to ___. (The number you selected that is divisible by three. How old is Hank? How old is his Dad?

Then, to jazz it up, make a simple chart for yourself with three columns:

PAST (A TIME BEFORE NOW), PRESENT(NOW), FUTURE (SOME TIME LATER).

And then write each person's initials or name along the side. So you could organize their ages by how old each was, for example five years ago, how old they are now, and how old they'll be in, for example, 20 years from now. Then you can really get complicated and fancy!

Good luck and happy Father's Day!

Hope this helps,

Mitch