A Better Deal

I love shopping for my girls nowadays and buying items in bright pastel colors that will brighten the monochromatic pallet of the winter. In the last couple of days we made a few special trips to pick warm boots and pants. At first I purchased a couple of toddler pants in a strip mall for a "buy one, get second one half price" deal:

Two days later I finally organized the baby's closet and realized I need many more warm pants for the day care and home. In a run-by shopping after a movie I bought three more colorful pairs at a different store that had a "buy 2, get 1 free" offer.

Taking all the tags off I realized that all the pants had the same original price. But what purchase was a better deal or were they all the same? Each of my older kids had a different opinion on that. What do you think?

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

The Shopping Cart Paradox

We all have done it thousands of times. But I have thought it through only now. There is a serious issue.
A paradox, I'd say. The shopping cart paradox...  The more you buy, the more pronounced this paradox becomes. You pay at the cashier, bag all your groceries and carefully place them in the shopping cart arranging the heaviest items on the bottom and anything breakable, smashable, squeezable on the top. If you do your family shopping only once a week and especially if you have diaper-age kids, chances are your cart is full to the top.

top: anything fragile, smashable, squeezable
bottom: heavy items

Now, you come to your car and start transferring the bags into your trunk. What bags are on top of the cart? The bags with the breakable, smashable, squeezable items!  The only choice you have is to put them at the bottom of your trunk. What goes next? The bags with the heavy items that will undoubtedly break, smash and squeeze the bread, yogurts, eggs and peaches on the bottom. You see the flipping grocery cart-car paradox? Of course you are aware of this. So, you naturally try to sort the bags as you place them, spreading the bags around the trunk or the shopping cart. Some of us are even using the ground or a second cart as a temporary placeholder, flipping the bag order once again: lighter to the ground, heavier in the trunk, then placing lighter ones on top. We make it work, but it is far from optimal. It seems that some creative solution is required here to save us all from this ridiculous weekly process.

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

Image by Polycart used under CCL.

A Pawn Stars Puzzle

My 12-year old son recently became a fan of the Pawn Stars TV show.  I have been trying to decide for a while what I think about this show. It is a Las Vegas Pawn Shop, run by three generations: an aging, cursing, revengeful dad; nice encyclopedically knowledgeable, cursing son, and a heavy, tattooed, Harley Davidson-riding, cursing grandson.  Just as I was about to tease our son for watching this strange thing, my dad (who is frequently with us helping me with the new baby) fell into the traps of the show too. What can I say. It is informative,  fast paced and the objects traded are very cool. So, here it is: a Pawn Stars Puzzle created in collaboration with my son.

A woman got the following objects at the Brentwood Estate Sale: a 16th century beheading sword and a diamond encrusted Rolex. A few months later she needed money and drove to the TV-featured Pawn Shop to trade these objects. She got $5,000 for each. On one of them she lost 15% as compared with the price she got it for, on the another she gained 15%.  Did she get even in this whole buy-and-sell adventure, or did she lose or gain money?

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

Fake Utensils

This puzzle celebrates our puzzle solver Annie, who quietly reached over the 10 puzzle mark.



In this puzzle Annie is Manhattan's top private detective and she is being called to Tiffany's jewelry store to help investigate a fraud. Tiffany's manager informs Annie that they sold 10 sets of the Tiffany & Co Silver Utensils yesterday to 10 different people. Each set consisted of 24 pieces, all of them of the same weight. It came to their attention that one of the sets was a fake set that was supposed to be used as a window display. All the utensils in this set weigh 1/10th of the silver utensils. Tiffany's manager wanted to avoid a scandal and notification of all the buyers of a potential fraud. However, she realized that all the buyers should be called back to the store (with their utensil sets) in order to detect and replace the fake set. She asked Annie for the fastest way of detecting which of the 10 sets is the fake one in order to minimize the commotion and suspicion.

Annnie told her: "Reach out to all the 10 buyers and ask them to come to the store with the utensil sets they bought claiming that they forgot a butter knife that should be matched to their specific set. Once I have all the utensils here, all I need is to use your weight scale one time only to detect which set is fraudulent. You will need to present these buyers with 10 butter knives to leave them satisfied."

Do you think Annie was over-confident? How could she avoid weighting each of the utensil sets and use the scale only once to find the fake set?

Answers accepted all day long on Friday May 27th and Saturday May 28th, 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.

Meet me at Marshalls

I love high quality discount stores like Marshalls, TJ Max or Filene's Basement. Nothing could beat the joy of finding a treasure for $20-30 without the guilt of overspending. I venture to Marshalls approximately once in two weeks, at a random day and time, spend there around 30 minutes and go home satisfied by my "shopping drug dose".

Slowly I started to realize that around half of the times that I shop there I run into the same mom from my kids' school. We both get slightly embarrassed, assuming that the other must be living there for our encounters to be so frequent. This mom doesn't work there or hang out there, in fact she seems to spend around 30 mins at the store, like I do.

I am wondering whether our high frequency of encounter means that she indeed comes there every day or that her shopping frequency is relatively rare like mine and it just so happens that our in-between-work-and-school shopping cycles and time tables frequently coincide.

Top image by o5com, distributed under CCL.

Answers accepted all day long on Friday April 1st, 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.

Which One Is Your Carpet?

Image by vshioshvili, distributed under CCL

Post-Holidays sales are here. You come to a home decoration store and splurge on a new carpet for your living room. When you drive to pick up the carpet at the back of the store, you see 3 different carpet rolls packed for shipping. Which one is yours? They all appear to have exactly the same type of carpet, all tightly rolled, and only vary by the size of the roll (base of the carpet cylinder). Can you figure out the length of the carpet from the diameter of the roll and size of the little empty hole in the center?

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.

Disposable Utensils: how many to buy?

Every time I organize a rather large party and decide to use disposable utensils, I am at loss how many plates, spoons, forks, knives, napkins and cups to buy. Two per person may be a very approximate guess. But we all know that there is more to it: there are usually many more knives left that forks, most of us will re-use their plate for another round of helpings but will not re-use the same glass for another drink. Running out of utensils may be a disaster for a party, buying too much is unnecessary expense and may mean another box for your already full storage closet. What is the smart party planning math you are using personally or professionally?

Enter your answer on our Family Puzzle Marathon page. Solve three and get a prize!

Obscure Product

How much is for one?
Two dollars, - replied cashier at the hardware store.
How much is for twelve?
Four dollars.
OK. Give me please nine hundred and twelve.
This will be six dollars.

What product were they talking about?
(from the book by M.Gardner)

Enter your answer on our Family Puzzle Marathon page. Solve three and get a prize!

Making the best of the L.L.Bean Sale

L.L.Bean is running a great holiday sale on the front page of New York Times:


Given these multiple discounts, I wonder if there is any purchase price at which it makes sense to split your order to enjoy separate gift certificates for each part, even if you have to pay for shipping. Let's assume that shipping is $5 for any size order. And of course it is free on orders of $75 or more as sale ad states.

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

Cell Phone Trade

You buy a cell phone and after some time decide to sell it on eBay for $24. Interestingly, in this deal the percent that you loose is equal to the original price of the cell phone. What was the original price of this cell phone?
This puzzle is almost 300 years old and was invented by a French mathematician Étienne Bézout. Cell phones were not invented back then, so he substituted them with horses :)

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

A Golden Dress

Puzzles are everywhere. They come in a teacher's note from school, in a form of decision about renewing your fringe benefits or just simply stare at you from a shop's window. Believe it or not! One department store's Holiday decorated window claimed: "Great dress is worth its weight in gold or silver." I was driving by, so not sure I got all the little details right. But the beautiful, T-shirt style, holiday dress was there, sparkling behind the ad. How expensive do you think this dress may be? The ad can't lie, right?

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

The Case of a Missing Dollar

You buy $60 worth of products at the store and give the cashier 3 x $20. The cashier is scanning your store loyalty card and congratulates you on receiving $5 off from your purchase. She then asks whether you would like to contribute to a local charity. You agree to give $2, and then she gives you the remaining $3 back.
So, overall you paid $60 - $3 = $57
There are also $2 you gave to the charity. $57 and $2 are $59 total.
But you started with $60, where is the additional dollar?

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

Flat screen paradise

We have finally decided to buy a flat screen TV. My husband thought that our current 27" box does not allow him to see all the details of the recent, tense and thrilling, football game. He is considering a giant 54" screen. Will this screen increase our viewing area by two?

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

Outlet Mall vs DWR

A wife returned home after spending 6 hours at the outlet mall.
She was holding three bags.
"What's the damage?" curiously inquired her husband.
"Well, the content of the third bag is worth $100. The first one is worth the price of the third bag plus half the price of the second bag. The second bag is worth the combined content of the first and the third bags," elaborated the wife.
"Funny thing" - said the husband. "I just spent the same online in Design Within Reach in just 6 mins."
How much did they spent?

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

Chewing Gum Treat

A kid comes to the store with his piggy bank. He does not have enough money to buy a colorful chewing gum that he really wants, so his mom lends him exactly the same amount as he already has. Kid pays $1 for the chewing gum, takes the change and leaves. On a second week, kid comes to the store with his dad. Again, he convinces his dad that he really deserves this colorful chewing gum, dad lends him exactly the same amount as kid has, kid buys the gum, takes change and leaves. On a third week, grandmother sponsors the kid in a similar manner. And on a fourth week, kid does this trick on his older sister. After borrowing from her and buying the gum, he has no more money left.
How much did he have in the piggy bank to start with?

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

Mother-in-law's Bag Fetish

Most of us have some kind of fetish. For me, it is hats and cups. For my friend, Jane, it is shoes. My mother-in-law, could not return from a store without buying a bag: red or brown, big or small, leather or plastic. She loves them all. However, she would deny her having a bag fetish and claim that she is using them all as gifts. So, judge by yourself.
When asked recently "How many bags do you have?", she answered:
"Three quarters of their number plus three quarters of a bag."
How many bags does she have and does she really have a fetish?

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

Neiman Marcus Sale Puzzle

A pair of designer shoes at Neiman Marcus was discounted 15%, and three months later an additional 30%. Spring came and, unexpectedly, the shoe designer got into the spotlight at the Paris design show. Daniel Marcus, who runs the Neiman Marcus store, immediately decided to increase the shoe price by 45%. Question is, would it have been better to buy these shoes when they just arrived at the store or now, after all the price changes?

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

How to afford a Prada bag

Three women are dying to get the Prada bag from the latest fashion show, but neither could afford to pay the $1,200 that the bag is offered for. First woman is saying: "If each of you two will give me half of what you have, I will have enough to buy the bag. We could then share bag proportionally to our investments." Second is saying: "If each of you will give me one third of what you have, I will also have enough to buy this bag." Then the third woman that stayed quiet all the time, said: "If each of you two will give me just one fourth of what you have, I could buy this bag." How rich each of these women is?
(believe it or not, but this puzzle is 500 years old!)

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

Three Clocks

Three antique clocks were put up for auction. The first lost one minute in every twenty-four hours; the second lost one minute in every hour; and the third didn't go at all. Which clock would you buy if you chose the one that showed the correct time most often? (from Logic Puzzles by the Diagram Group)

Shop till you drop

You celebrate the Spring by heading shopping with your friend and agreeing on a maximum cash amount you can spurge. In the first store - Macy's - you spend half the money. In Nordstrom you spend four fifth of what you had left. In Lord-and-Taylor you spend five sixth of what was left. At that point you have load of shopping bags and only $5 left, just enough to pay for coffee and cake before heading home. How much money you started out with?

Like shopping? Try this story from TheMathMom: Shopping Math Or, How To Convince Yourself Into Buying Anything You Want