Question Dear Mitch, You said you'd have the answers to the Father's Day questions posted by "early evening". I live on the East coast of the United States and it's now almost 8:30. Can you please post them soon? Thanks, Charles Y. East Coast of the U.S. Answer Dear Charles, My apologies about the timing of this; we had technical difficulties due, I think, to some major lightning yesterday. (I'm currently living in a county that is sometimes referred to as "the lightning capitol of the world"). (NOTE: For people who did not tune in yesterday, they will not have to click back and forth to find out what the questions are that we are answering, because I have attached yesterday's complete question and answer at the very bottom of today's answer. Answers:1. Using the 'hint' I gave yesterday we do this: 90 divided by 3, and we get 30. Joe, the son, is 30. His Dad is 30 x 2, or 60. 2. Same pattern: 75 divided by 3 = 25. Son = 25. father = 50. 3. Here you can skip step one of the pattern from numbers 1 and 2 and realize that if they were each 6 years younger then together they're 12 years younger and their ages would've added up to 72. 4. In a problem like this if you try rearranging the sentences the task can become much simpler. Right now (present) = 92 Future: (5 years) = 92 +5 + 5 = 102. Next, you divide 102 by 3, and you get 34. SO: Son = 34. Father = 68. 5. Again, taken out of order we learn that Coolunim is younger than 40 and older than 30, and is a prime number. That leaves two possibilities: 31 and 37. If 31. then six years from now they will be 37 and 74. 37 + 74 = 111/ That answer fulfills all the requirements I gave for the answer, so there's no reason to even bother with the other choice, which was 37 NOTE: MY APOLOGIES: My question contained a mistake. It said that the sum of their current ages was a multiple of 3 and a multiple of nine. That sum, which is 93 is indeed a multiple of 3 (31 x 3 = 93). But it is NOT a multiple of 9. I don't know what I could have been thinking of! After all, 99 is a multiple of nine, and that's only six away from 93, so... 6. For this type there is a technique (or 'trick') which comes in handy: Whenever you are given the sum of two numbers and their difference, you simply take the sum, break it in half, write down that number (the number that is half the original number) on the left side of your page and again on the right side of your page. Then take the difference (here 24 years, and break it in half. You get twelve. You add twelve to one side and you subtract 12 from the other side. So you have 33 on the left and 33 on the right and you add 12 to one of the 33's and you subtract 12 from the other 33. And you get 45 and 21. Next the problem states that the grandfather is four times as old as Susan. So, 4 x 21 = 84. Her grandfather is 84 years old. And that's it! Hope this helped, Mitch Yesterday's Question and answer: 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 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. QUESTION 1: Joe's father is twice as old as Joe. Together their ages add up to 90. How old is Joe? QUESTION 2: Mike's father is twice as old as Mike. Together their ages add up to 75. How old was Mike six years ago? QUESTION 3: 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? QUESTION 4: 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? QUESTION 5: 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? QUESTION 6: 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, Michael, 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!   © 2021. Mitch Adler. All rights reserved.