Party Head Count

A few months ago we celebrated our son's Bar Mitzvah party. This was the first large-scale formal celebration that was held not in our back yard (unlike our wedding and a few other big bashes we have had). And the food was not the usual potluck or Trader Joe's or grilled meat, but a pre-tasted catering selection. I spent a month picking a place with nice vibe, good views, reasonable food and price, and plentiful parking space.  And, by the way, the place was half-a-way across the globe, in Israel, where most of our family and quite a few friends live. We celebrated in Tel Aviv, on the banks of the Yarkon river, in the restaurant space of the Daniel Amihai Rowing center, which looked magnificent in the evening and had even better views from inside, of the city skyline and Mediterranean sunset.

About a week before the event we had to provide the exact head count.  We were told that this would be the minimum amount of people we will pay for. Even if only half of these guests will show up, we will have to pay for the ordered amount as the chef will prepare the food for that amount. Should a few extra guests pop up, we will  pay for each of their portions as well, on top of the agreed upon amount. Inexperienced in such situations and dealing with relatives that we haven't seen in a while and customs we are no longer used to, we were not sure how exactly to estimate the expected head count most precisely. We invited 120, but how many will show up? The answer seemed to lay somewhere between 70 and 125.

Price-per-person depended on the number of people we reserve for:

less than 100 guests - $80 each
more than 100 guests - $64 each

in addition to the price-per-person, there was a service fee:
$100 for each waiter that serves 10 people
the more people will show up, the more waiters we would need

We tried to call and email everyone (no RSVP customs in Israel) carefully inquiring who is coming, but then we realized that some mathematical thinking and less precision could save us some money and time. How?


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

What is Wrong with This Prudential Ad?

Prudential is running a new advertising campaign titled "Let's get ready for a longer retirement"
The text under the picture says:
A typical American city. 400 people. And a fascinating experiment. We asked everyday people to show us the age of the oldest person they've known by placing a sticker on our chart. Living proof that we are living longer. Which means we'll all need more money to live in retirement. and so on.

While I agree that statistically we are living longer than our predecessors and we need to save more for our retirement, I doubt this experiment proves it.

I can imagine how it all came to be:
- Folks, let's emphasize that we are dying at an older age, and need to save more.
- But, Bob, we cannot talk about death in an ad campaign.
- Yeah, let's find something positive in us growing older, sicker, lonelier, absolutely dependent.
- Well, everyone is excited to hear about someone in the stress-less mountains making it to a 100.
- Great idea, let's talk about the oldest person you know!

So, why this chart is not a living proof of us living longer?

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

End of the World Puzzle

This puzzle celebrates our 10-puzzle points winner going under the code name "Jerome's wife" but the Canadian authorities revealed to me that her real name is Mary.

Expecting the approaching end-of-the-world and half-wishing and half-fearing that the company she is working for will be wiped away from Earth, Mary decided to ask for her December salary up-front.  She usually gets $10,000 monthly.  After some negotiations the accountant agreed to pay her $7,000 for the first three weeks of December stating that she also already got the Holiday bonus and together this will be a fair pay for three weeks out of four proportionally.   

The question is what is Mary's Holiday bonus?
Submit your answer anytime up until the dooms day, Friday the 21st.
End of the world image by Anthony Citrano, distributed under CCL.

A Special October?

This October is very special. It has 5 Fridays, 5 Saturdays and 5
Sundays all in 1 month. This happens once in 823 years. These are known
as money bags. Pass this along to 8 good people and money will appear in
4 days based on the Chinese Feng Shui. Those who stop it will experience
none.

Well,I received this message over 4 days ago and no money appeared so far. I am sending it now to over 1,000 good people and will let you what comes. While we may not be able to predict the fortune, I think we can check whether this October is indeed as special as stated: Is it true that October that has 5 Fridays, 5 Saturdays and 5 Sundays happens only once in 823 years? Seems suspiciously rare

Mathematician in the Law School

Our most celebrated puzzle-solver, Kim the Ingenious, decided to attend a prestigious law school. With her sharp mind, clear logic and great persuasion abilities, she managed to convince the Law School administration to sign up for a deal. This deal would contractually oblige Kim to pay double the school fees, but only when she wins her first case. Until then, she would be required to pay nothing.
However, what Law School administration did not know was that Kim only ever intended to take on cases that she could not possibly win. As soon as she entered the Bar, she chose only those clients who have committed their crimes live on national TV and then sighed a confession in front of millions of people.

Unfortunately for Kim, the new dean of the Law School she attended, Prof Protagoras, was not prepared to tolerate her shenanigans any longer. The Professor came up with a plan every bit as devious as Kim's. He decided to sue Kim in court for the money she owes.

Professor does not expect the law school to win the case, but he believes that it will end up getting its money anyway. He reasons as follows: if Kim wins, then she will won her first case, which means she will be obliged to pay the amount she owes. If she doesn't win, then it means court has confirmed that she has to pay the money. Either way, Law School gets paid.

Needless to say, Kim does not see it quite like this. She believes that if she wins the case, it means the court has determined that she doesn't need to pay the money. If she loses, she has still not won her first case, which means that she is not obliged to pay. So, either way, the law school does not get paid.

Which of the two of them has got it right? And why?
This intriguing puzzle was adapted from a great book by J. Stangroom "Einstein's riddle."

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The best deal on a plane ticket

Summer is a time of vacations and many of us have been or will be purchasing plane tickets for these long-dreamed-about trips. I usually look for a minimum number of stops, convenient hours, not too short and not too long a layover, and a familiar airline. Then, I go for the cheapest selection on this list. The difference between the least expensive choice and the next one is usually around 5%. That can be $50 for an International flight or $15 for domestic. Sounds like a good strategy, right? On my recent trip I was not so sure about that.
My least expensive choice didn't have personal TV screens in front of every seat, something that became very common on large planes and long international flights. On the way back, audio, light and even flight attendant buttons didn't work for the whole row of seats I was in. Toilets were dirty, food bad, flight attendants not very courteous. There were no eye cover and comfy socks that I know are being offered (or have been a year ago) on the airline that was next in price. Long-distance flights are never easy but for parents-flying-solo they can be rejuvenating: read, eat, watch, chat and sleep. Just yourself to worry about for a few hours or perhaps even a whole day. Quantifying all the things I expected but didn't get on my last trip, I am wondering whether this $50 difference was significant.

Perhaps I should adopt the same strategy as in a restaurant wine selection rule: pick second from the least expensive and you won't miss. What do you think?

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Easy Money

Years ago a blacksmith put a set of new shoes on a horse owned by a wealthy but stingy rancher. When the job was completed, the blacksmith charged the rancher ten dollars for the job. The rancher claimed the price was too high and refused to pay.
"Very well," the blacksmith told him, "I'll make a deal with you. Each horseshoe has eight nails. There are four shoes on the horse. Four eights are thirty-two. I'll charge you one cent for the first nail, two for the next, four cents for the next, and so on for all thirty-two nails."
The rancher agreed at once and reached for his wallet. How much will he have to pay?

This puzzle is from "Puzzle it out" book by Richard and Churchill.

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Sam Loyd's Cashier Puzzle

This puzzle comes from one of the greatest puzzle makers, Sam Loyd, who lived over 100 years ago. It tells of an old man who stepped into a bank with a check for $200 and asked the cashier, "Give me some one-dollar bills, ten times as many twos, and the balance in fives!"

How did the cashier perform this transaction?

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Stumble with Toonies

Rumors have it that the longest line in the Canadian Olympic village assembled at a supermarket when a customer purchasing $37 worth of produce realized that his wallet contains only $5 bills while the cashier only had $2 coins, nicknamed Toonies. Is it possible to fairly process this transaction without forcing this customer to buy $3 worth of bubble gum?

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New York Devil

A man from New Jersey was complaining that he doesn't have enough money. A devil descended from the sky and offered a deal to this man:
"Feel all this cash you have in your wallet? I can double it every time you cross George Washington bridge from NY to NJ. However, when you cross the bridge in the other direction you have to pay the $8 toll."
The man quickly agreed, but was left without any cash after just four trips.
How much cash did he have to start with?

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Inheritance Puzzle

One real estate magnate left three mansions to his five sons. Unable to figure out how to divide three by five, they went to an estate attorney. Attorney recommended that three older brothers will take one mansion each and that each would pay $800,000 to the youngest brothers, making inheritance equal. How much worth are the mansions?

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HR Quiz

You want to hire a temporary employee for one month. You offer him reasonable wages, but the employee suggests an alternative. For the first day of work, he will be paid a penny. For the second, two pennies. For the third, four pennies. The salary for each subsequent day will be double the previous day's, until the one month term is over. Ignoring the legalities of such a situation, would it be a good idea to accept the potential employee's proposal?

(this great puzzle is from World's Best Logic Puzzles book by Seven Treasures Pub.)

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Design Your Own Shlumpies

Imagine you are an empress or emperor of a new kingdom and you need to introduce a new currency named Shlumpies. You call your Minister of Finance and ask her to design paper bills for Shlumpies. What is the minimal number of different denominations that you need to design, if you want to be able to pay any number of Shlumpies (up to a 100) using no more than three bills of each type?

For example, in the US kingdom we have $1, $2, $5, $10, $20, $50 bills. You can pay any dollar amount (up to a $100) using up to three bills of each type. Your kingdom is trying to be superior, managing with less types of bills. Can you do it?

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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?

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Summer Produce

5 pounds of summer squash and 2 pounds of strawberries cost $10.
2 pounds of summer squash and 5 pounds of strawberries cost $11.
How much would you pay for 1 pound of summer squash and 1 pound of strawberries?

Three friends

Three friends want to buy a house that costs $520,000 together. All friends have the same salaries. First one promised to contribute one half of his salary to the house purchase, second friend promised one third of his salary, and third friend one fourth of his salary. How much was given by each friend?

Two rich friends

One friend is saying to another: "If you give me $100, I will be twice richer than you." To this, second friend replied: "If you give me $10, I will be six times richer than you." How much each of the friends has? (from the old Russian puzzle book)

Spring Jacket

Spring weather is finally here and you decide to bring your light jacket out from the basement storage. In its pocket you find $3.60, all in quarters, dimes, and pennies, equal number of each. How many of each type of coins are there?

The King's Salary.

After the revolution, each of the 66 citizens of a certain country, including the king, has a salary of $1. The king can no longer vote, but he does retain the power to suggest changes - namely, redistribution of salaries. Each person's salary must be a whole number of dollars, and the salaries must sum to $66. Each suggestion is voted on, and carried if there are more votes for than against. Each voter can be counted on to vote "yes" if his salary is to be increased, "no" if decreased, and otherwise not to bother voting.

The king is both, selfish and clever. What is the maximum salary he can obtain for himself, and how long does it take him to get it? (from P.Winkler, loosely inspired by real historical events in Sweden)