The last brain teaser I posted seemed to be rather popular. Therefore, let's do another one.
This is a mathematical brain teaser pulled from the book "Mathematical Brain-Teasers" by J. A. H. Hunter and published by Dover Publications, Inc. in 1976.
The puzzle is entitled The Insurance Agent:
"So you're just forty," said Bill, flipping the pages of his rare book. "With three kids, eh? How old are they?"
"Lay off. You're not insuring them too." Bert laughed. "But figure it out for yourself. Their three ages add up to the number of this house, and multiplied together they make my age.
Bill thought hard. "I get what you mean, but I still can't tell their ages for sure."
"Forget it then," Bert told him, glancing at his watch. "The two older kids will be walking back from school now, so you'll meet them."
That was all Bill needed to know, and he gave the three ages without further delay.
What are they?
See below for the answer.
ANSWER:
There are several possibilities but only two make sense. The five possible combinations of ages are:
20,2 and 1;
10,4 and 1
10,2 and 2
8,5 and 1
5,4 and 2
I originally answered 5,4 and 2 which makes the house number 11. (5 X 4=20 20X2=40 which is Bert's age). The answer given in the book is 8,5 and 1. (8 X5=40 40X1=40 and this answer makes the house number 14).
The key clue to the puzzle is where Bert says the two oldest kids are walking home from school now. While 5, 4 and 2 is still possible, it is unlikely a 4 year old would be in school at that age. Therefore, it is more likely that the 8,5 and 1 answer is correct. A five year old could certainly be in kindergarten at that age and be walking home from school. The other options would only have one school age kid with the 20,2 and 1 option possibly having none.
How did you do?
Tuesday, July 9, 2013
Thursday, March 28, 2013
STILL SETTLING IN
It's been six months now since we sold our home of 27 years and moved into a townhouse. While we have made considerable progress, we are still not entirely settled in. Clearly we misjudged the difference in space from the old house to the new townhouse. We also underestimated the amount of work needed to be done.
The old house was certainly not a mansion or even huge. It was about 2100 square feet. We also had a full basement and a two car garage. We bought the house in 1986 from my wife's mother. My wife had lived in the house for 47 years so I expected that the move might be hard on her. I was wrong. We both love the new place and the lack of maintenance. However, the new place is only 1400 square feet but that is still a third smaller as the old house. Even though we downsized quite a bit, it wasn't enough. The basement is also smaller and even though we have a two car garage, it is a smaller two car garage. My bad.
Living in a townhouse, much of our outdoor maintenance is taken care of through our association fees. I certainly don't miss shoveling snow and raking leaves. Our driveway was about a 150 feet long. We also had the beautiful old oaks that were over 200 years old on the property and it took about 75 bags each year to bag the leaves. I do miss the garden and mowing the lawn, which I found to be therapeutic. I also loved the English Tudor style. I am often asked why we sold. Well, the kids are gone and there is only the two of us now and who knew we needed all that space. But, the biggest reason was the property taxes. We paid over $10,000 a year on property taxes and if I were to ever to retire, we could no longer afford those taxes. Our taxes now are about a third of that. Quite a difference. It is criminal what we pay out in property taxes, most of which go to the schools, and certainly isn't a fair formula.
We still have some projects remaining at the new place. Next up will be finishing the basement. That will make a big difference in our lives and enable us to finally fully unpack. Next will be adding ladder/stairs to the attic. This was a surprise. We have substantial usable space in the attic and it has electrical and lighting up there. We need to add the pull down stairs/ladder for access and put a floor up there and we are good to go. Perfect space for storage which we need. This summer we will continue putting hardwood floor in the house. We put hardwood floors or ceramic tile throughout the downstairs right after we moved in. Next we will do the stairs going up to the second floor. That should make a difference. Doing the upstairs will be more problematic because we have everything in place and would have to move it to put in the floor and it requires about two weeks for the entire process. We have no where to store this stuff for such a long period of time. We may have to do it piece meal.
This post is a little different than what I usually write but I hope you find it amusing nonetheless.
The old house was certainly not a mansion or even huge. It was about 2100 square feet. We also had a full basement and a two car garage. We bought the house in 1986 from my wife's mother. My wife had lived in the house for 47 years so I expected that the move might be hard on her. I was wrong. We both love the new place and the lack of maintenance. However, the new place is only 1400 square feet but that is still a third smaller as the old house. Even though we downsized quite a bit, it wasn't enough. The basement is also smaller and even though we have a two car garage, it is a smaller two car garage. My bad.
Living in a townhouse, much of our outdoor maintenance is taken care of through our association fees. I certainly don't miss shoveling snow and raking leaves. Our driveway was about a 150 feet long. We also had the beautiful old oaks that were over 200 years old on the property and it took about 75 bags each year to bag the leaves. I do miss the garden and mowing the lawn, which I found to be therapeutic. I also loved the English Tudor style. I am often asked why we sold. Well, the kids are gone and there is only the two of us now and who knew we needed all that space. But, the biggest reason was the property taxes. We paid over $10,000 a year on property taxes and if I were to ever to retire, we could no longer afford those taxes. Our taxes now are about a third of that. Quite a difference. It is criminal what we pay out in property taxes, most of which go to the schools, and certainly isn't a fair formula.
We still have some projects remaining at the new place. Next up will be finishing the basement. That will make a big difference in our lives and enable us to finally fully unpack. Next will be adding ladder/stairs to the attic. This was a surprise. We have substantial usable space in the attic and it has electrical and lighting up there. We need to add the pull down stairs/ladder for access and put a floor up there and we are good to go. Perfect space for storage which we need. This summer we will continue putting hardwood floor in the house. We put hardwood floors or ceramic tile throughout the downstairs right after we moved in. Next we will do the stairs going up to the second floor. That should make a difference. Doing the upstairs will be more problematic because we have everything in place and would have to move it to put in the floor and it requires about two weeks for the entire process. We have no where to store this stuff for such a long period of time. We may have to do it piece meal.
This post is a little different than what I usually write but I hope you find it amusing nonetheless.
Tuesday, March 26, 2013
Answer To Brain Teaser
The previous post presented the problem of the "clever cook". Now, I will give you the answer.
Pour the five-ounce container full from the jug. Pour the three-ounce container full from the five-ounce container, leaving two ounces in the five-ounce container. Pour the three-ounce container back into the jug. Then pour the two ounces remaining in the five-ounce container into the three-ounce container. Pour the five-ounce container full from the jug. Fill the remaining one ounce of the three-ounce container from the five-ounce container leaving four ounces in the five-ounce container.
Pretty clever. Did you figure it out? Hopefully, you enjoyed this little exercise and maybe I'll do it again.
Pour the five-ounce container full from the jug. Pour the three-ounce container full from the five-ounce container, leaving two ounces in the five-ounce container. Pour the three-ounce container back into the jug. Then pour the two ounces remaining in the five-ounce container into the three-ounce container. Pour the five-ounce container full from the jug. Fill the remaining one ounce of the three-ounce container from the five-ounce container leaving four ounces in the five-ounce container.
Pretty clever. Did you figure it out? Hopefully, you enjoyed this little exercise and maybe I'll do it again.
A LITTLE BRAIN TEASER
Today, let's do something completely different. Jim Fixx was the author of "The Complete Book of Running" which helped start the running/jogging craze. Unfortunately he did of a heart attack at age 52. Jim Fixx was not only an exercise advocate, he was also a very smart individual. He was a member of Mensa which is the club for high IQ individuals. Along those lines, he also wrote a book titled "Games For The Super-intelligent" which was published by Doubleday in 1972. The book is full of all kinds of games and puzzles that will have you scratching your head for hours. Today, I want to pose one of those problems for you. I will give you the answer in the next post so no looking and good luck.
Case Of The Clever Cook
A camp cook wants to measure four ounces of vinegar out of a jug, but he only has a five-ounce and a three-ounce container. How can he do it?
Seems simple doesn't it. Have at it.
Case Of The Clever Cook
A camp cook wants to measure four ounces of vinegar out of a jug, but he only has a five-ounce and a three-ounce container. How can he do it?
Seems simple doesn't it. Have at it.
Thursday, February 14, 2013
CATCHING UP
It's been some time since my last post which I believe involved football. My Ohio State Buckeyes went unbeaten but were on probation so couldn't play in a bowl game. That's unfortunate because it likely would have been an Ohio State versus Notre Dame national championship.
Mount Union went unbeaten and won their 11th Division III National Championship. The good news ends there unfortunately. My high school went winless and I think Valparaiso University only won one game. The Browns won five but the future is bright.
My current project is getting our new town house we bought in September ready. The townhouse is very nice but is much smaller than our previous home. I thought we had downsized sufficiently but I was wrong. As such, storage is an issue.
We just discovered something that has been around for over 40 years, Ikea Billys. These are modular book cases that attach to the wall and each other to form what appear to be built ins along the wall. When attached to the wall and each other they are really quite stable. The foot print is small only coming out 11 inches from the wall, they even have notches along the back of the units where they stand up against the wall for any base molding you might have. This insures they are flat and snug against the wall. They have doors, both glass and panel, so that they can form cabinets if desired. They also contain DVD towers which will certainly be helpful. We have a long wall perpendicular to the loft and between the bedroom which will be perfect for them. The run is about 10 1/2 feet long which will provide us plenty of storage for our photos, books, CD's and DVD's. What's great about these units is that you can also purchase height extenders that fit on top of the various unit and extend the height to any level you want. In our case, we are extending them to within 3 inches of the ceiling. Our ceiling is 8 feet high.
We obtained the various components needed to complete our run in the different configurations we wanted. We decided on the birch veneer finish, there are five choices, and they look great. The best part of it is the cost. Sure they are particle board and fiber board and not solid wood. As such they tend to be a little heavy which can create a problem assembling them because of the weight. But the cost can't be beat. The cost for our run which includes a regular 32 inch bookcase, two DVD tower, three 16 inch bookcases and a 32 inch bookcase that we put glass and panel doors on, with the height extenders, was about $650. What a bargain.
If anyone has had any experience with Billys, please let me know. I would love to hear about your experiences. Now its on to basketball and hockey now that football is over. Fortunately the NHL strike is over and the Chicago Blackhawks are off to their best start in franchise history, which is a very long time. The Blackhawks were one of the original six teams that formed the NHL. Ohio State and the B1G is loaded with teams which makes for some great games. It won't be long until the conference championships and March Madness.
Mount Union went unbeaten and won their 11th Division III National Championship. The good news ends there unfortunately. My high school went winless and I think Valparaiso University only won one game. The Browns won five but the future is bright.
My current project is getting our new town house we bought in September ready. The townhouse is very nice but is much smaller than our previous home. I thought we had downsized sufficiently but I was wrong. As such, storage is an issue.
We just discovered something that has been around for over 40 years, Ikea Billys. These are modular book cases that attach to the wall and each other to form what appear to be built ins along the wall. When attached to the wall and each other they are really quite stable. The foot print is small only coming out 11 inches from the wall, they even have notches along the back of the units where they stand up against the wall for any base molding you might have. This insures they are flat and snug against the wall. They have doors, both glass and panel, so that they can form cabinets if desired. They also contain DVD towers which will certainly be helpful. We have a long wall perpendicular to the loft and between the bedroom which will be perfect for them. The run is about 10 1/2 feet long which will provide us plenty of storage for our photos, books, CD's and DVD's. What's great about these units is that you can also purchase height extenders that fit on top of the various unit and extend the height to any level you want. In our case, we are extending them to within 3 inches of the ceiling. Our ceiling is 8 feet high.
We obtained the various components needed to complete our run in the different configurations we wanted. We decided on the birch veneer finish, there are five choices, and they look great. The best part of it is the cost. Sure they are particle board and fiber board and not solid wood. As such they tend to be a little heavy which can create a problem assembling them because of the weight. But the cost can't be beat. The cost for our run which includes a regular 32 inch bookcase, two DVD tower, three 16 inch bookcases and a 32 inch bookcase that we put glass and panel doors on, with the height extenders, was about $650. What a bargain.
If anyone has had any experience with Billys, please let me know. I would love to hear about your experiences. Now its on to basketball and hockey now that football is over. Fortunately the NHL strike is over and the Chicago Blackhawks are off to their best start in franchise history, which is a very long time. The Blackhawks were one of the original six teams that formed the NHL. Ohio State and the B1G is loaded with teams which makes for some great games. It won't be long until the conference championships and March Madness.
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