New House Puzzle

A man just finished painting his house and needs something more.
At the hardware store the clerk shows him what he wants and says, "one is $1."
"Fine," says the man, "I took 600, so here's $3."
What had he bought?

image by Padre MarianOne, distributed under CCL.

this nerve-wrecking puzzle is from The Mensa Genius Quiz Book but you don't need to be a genius to solve it. The House painting is a hint. Stand in front of your front house/apartment door and think what possibly can cost one for $1 and $3 for 600.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Optimal Washer and Dryer Location

Imagine that you are building a 3-story house in suburbia. The traditional layout - bedrooms on the top floor, salon+living room+kitchen on the main floor and whatever you need (computers, play room, guestroom ) in the basement. Where would you place the utility room with the washer, dryer and ironing station?

This may seem like a simple household planning task, but as with many other household tasks, there is a surprising math problem hiding inside.
There are quite a few variables to consider:

1. distance each member of the household needs to walk to bring dirty laundry to the basket
2. distance between the basket and the washer
3. distance one needs to walk to deposit the laundry, then switch from washer to dryer, then take the clothes out
4. distance one needs to walk to sort the folded laundry to the shelves

All these variables may have different weight depending on the number of people in the household, size of the washer, and slope as walking downstairs is usually easier than going up.

What are your thoughts on this problem?

I have lived in a house where laundry room was in a basement but the Distance #1 was minimized by having a laundry chute all the way from the bedroom floor to the basement.  Therefore D1 and D2 were close to 0. D3 was an OK run 20' down the stairs from the main living space times 3 (to deposit the laundry, switch to the dryer and take it out). However, D4 was a problematic hauling of the heavy folded laundry two floors up.

Since then I have seen people claiming that laundry room should be on the same floor as the bedrooms to make D1 and D4 simultaneously minimal. And I have met people who were convinced that laundry room should be right next to the kitchen that will minimize the D3.  

How do you optimize this in your house?

Image by sbluerock, distributed under CCL.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

How Tall is Your House?

Imagine that you are shopping for a house and a Real Estate agent takes you to an amazing contemporary that looks something like this:

You inspect the house and climb up on top of the roof. You would like to know how tall the house is because a new law allows owners in this area to add another floor if the height of the house is below 10 meters. Unfortunately, blueprints with the specified height couldn't be found. Are there any experiments you can do to measure the height of the house? There may be more than one answer.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

A Better Soap

In our family's recent stay at a hotel in Maine, we found the following peculiar soaps in our bathroom.


Do you think mice ate the centers of the soaps, or the design is intentional? Does a soap with a hole in it have any advantages over the traditional fully-filled oval-shaped soap? Can you suggest any improvement to this design that can make this soap even more advantageous?


Answers accepted all day long on Friday June 10th and Saturday June 11th, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who solved it will get a puzzle point. Please, explain your answer.

New Kitchen Chairs

This puzzle celebrates our 20 puzzle point solver - Wang. It goes like this:
Wang and a friend have been shopping for new kitchen chairs. They went to a few stores, tried sitting on the wooden chairs, plastic chairs, aluminum chairs, counter stools and bar stools. To their surprise they found most of the four-legged chairs less stable than most of the three-legged chairs that they sat on. Wang has been contemplating about this all the way home and suddenly it occur ed to him that there is mathematical truth behind their empirical observation. What is it?

Top image by Fernando G., distributed under CCL.

Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who contributed something reasonable will get a puzzle point. Please, explain your answer.

Enormous Lot

Over drinks in Vegas one Real Estate developer has been boasting about an enormous piece of land he got in Montana. According to the developer his land was in the shape of a triangle. One side of the triangle reached 200 miles from end to end. On each of the other two sides lot extended 100 miles from corner to corner. All of the listeners were impressed except for one. That woman merely laughed and said, "Why a lot of that size wouldn't even have to pay taxes where I come from."
Strangely enough, this woman was correct. How could this be so?

This puzzle is adapted from a book "Puzzle it out" by E. Richard & L. Churchill.

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

Tile Adventures - Continued

We are doing renovations at home and a few weeks ago I posted a puzzle about the number of tiles we should buy. We planned on using two sizes of the same tile: 6"x6" and 12"x12" in the pattern depicted below:



With your help, I calculated the number of tile boxes to order; the tiles arrived; we proudly showed them to our contractor; and he said: "That's not good. The pattern is not going to work."
We ended up with a slightly different pattern that I copied from Lowe's bathrooms. Here are our new tiles (still without the grout). Can you guess why we couldn't use the original pattern as planned?



Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

How many tiles to buy?

Did you encounter any puzzle last week? Feel free to share it with us. Here is one that we stumbled upon figuring out the amount of tiles to buy to replace the old wood floor at the door entry. The area we want to cover is approximately 90" X 150". We want to use a pattern combining tiles of size 12" x 12" and 6" x 6". One large one and two small on top, creating together a rectangle of 12" x 18". Large tiles are sold in boxes, each holding tiles to cover 10 square foot. Smaller tiles are sold in boxes that each holds tiles to cover 6 square foot. How many boxes of each should we buy?

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

Messy Socks Drawer

Your messy socks drawer has twenty four socks. Six of them are brown, six are black, six blue and the remaining six are red with white stripes. How many socks must you take out of the drawer, without looking, to be sure of having a matched pair of any color?

Photo by bahkubean, distributed under Creative Commons license

This is a puzzle from The Mensa Genius Quiz Book 2 by M. Grosswirth and A. Salny. But you really do not need to be a genius to solve this one. Stated differently: you are probably cracking puzzles like that every day and never guessed you are a genius.

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

Open Mike: dishwasher vs washing machine

This has been bothering me ever since we became homeowners and perhaps you could help me figure it out. Why does it take washing machine 10-15 mins to do the laundry while dishwasher works for an hour? Our dishwasher and washing machines happen to be of the same brand. They both do pretty good job of removing the dirt. In both cases, the dirt mostly comes from the same source - food. You know, kids...
When doing dishes or laundry by hand, it takes approximately the same amount of time. Right?
Why does it take 3-4 times longer for a dishwasher to clean the dishes from the same food, than it does for the washing machine to clean the clothes?

Let's have an "open mike" style conversation here. No answer is wrong, any ideas accepted. Perhaps we could even patent something :)
Enter your ideas Family Puzzle Marathon page.

Tile Paradox

Have you ever had to buy tiles for your kitchen or bathroom floor? Then, you have heard a rule of thumb that you need to buy 15% more tiles if you are planning to install them diagonally. Does it really make sense? Your floor area is constant. All you need is to measure your floor area and divide by the area of one tile. This gives you the amount of tiles you will need. It shouldn't matter how you position them, they still should sum up to the area of your floor. Right?

Submit your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

One mower is good, two or three are even better

Imagine that you own a large castle in a countryside and preparing to host a big party there in a couple of days. For the party, you need to mow all the grass around your castle. You took Yellow Pages and called in three local gardeners. First of them told you that it would take him one whole week to mow all your grass. Second told you that it would take her two weeks. And a third one promised to do it in three weeks. In a hurry to get ready for a party in time, you hired all three of them to work in parallel. How long would it take for them?

Photo by Bobasonic, distributed under Creative Commons license.

Submit your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

Paint Job

One painter could paint the house in 14 days. When working together with his son, he could paint the house in 10 days. How many days would it take to paint the house, if the painter's son works alone?