## Monday, May 13, 2013

### Mother's Day Math

Problem: On Mothers day (May 12 this year) restaurants are very crowded because many people take their mothers, grandmothers, great-grandmothers, etc out to lunch. (Grandparents day is in September but I think most people ignore that and honor their grandmothers on mothers day and their grandfathers on fathers day.)

My solution: Take mom out to lunch the FOLLOWING week. Some of my friends tell me NO- you can't just MOVE Mothers day- what are you--- The Master of Space and Time? The key is that my mom AGREES with me and in fact raised me with these values: (1) Never do X when everyone else is doing X, its too crowed, and (2) Learn the polynomial VDW theorem.

While this solution may work for me, it may not work for everyone. Here are some options to alleviate the restaurant crunch:

1. Declare the second WEEKEND in May to be MOTHERS WEEKEND. People take their moms out to lunch SATURDAY or SUNDAY. This would split the restaurant load in half.
2. Declare May MOTHERS MONTH. People take their moms out to lunch ONE Sunday in May. This would split the restaurant load by 4.
3. Declare May MOTHERS MONTH. People take their moms out to lunch ONE Saturday OR Sunday in May. This would split the restaurant load by 8.
4. Declare May MOTHERS MONTH. People take their moms out to breakfast OR lunch OR Dinner ONE Saturday OR Sunday in May. This would split the restaurant load by 24.
How would people DECIDE which day to do:
1. The last day of April have mom either (depending on which of the above schemes) flip a coin, role a 4-sided die, or role an 8-sided die or role two 12-sided dice to determine which day to be taken to lunch. Fortunately, due to the Dungeons-and-Dragons craze that girls got into about 40 years ago, most mothers have these dice. But in case she does not, here is a nice MATH PROBLEM (I am sure already solved): USE fair coins and fair 6-sided dice to simulate other random choices fairly. In our case 4-sided, 8-sided, and 24-sided. Which random choice can be simulated? Which can't?
2. Say we do the Saturday/Sunday/breakfast/lunch/dinner solution. Everyone with last name beginning with A goes to breakfast on the first Saturday. Everyone with last name beginning with B goes to lunch on the first Saturday. etc. There are only 24 lunches and 26 letters, so merge P and Q, and merge Y and Z.
How likely is any of this to come about? It would need to evolve naturally as a social custom. It also would have to not be that hard to implement. As such the 24-meal-plan probably won't catch on. Also, if Mother's Day become Mothers one-of-24-meals-day it may lose something. Hence the 2-meal-plan solution is probably the best.

However, the entire tradition of taking mom out to lunch on mothers day may fade. The origin is that mom cooks for the family most days, so this ONE day they take her out. Nice! But more and more households share responsibilities (NOTE- I have no facts or stats to back this up but it has a certain truthiness about it) hence the notion of taking mom out to lunch may seem more and more odd over time. Then again, its still nice being taken out to lunch.

#### 5 comments:

1. Rolling 2 12-sided dice to get a 1 in 24 result only works if you can distinguish the two dice: you'll have 144 different outcomes, and can map groups of 6 to the 24 wanted results; rolling a 4 sided and a 6 sided die may work better.

As for simulating the 4, 8 and 24 sided dice: the 4-sided one can be simulated with 2 coin flips; the 8-sided die can be simulated with 3 coin flips; and the 24 sided die with 2 coin flips and a roll of a 6 sided die.

If you are willing to accept the result of "reroll" on some outcomes, you can simulate any sided die with just coin flips, or rolls on a 6 sided die. For instance, to simulate a 4-sided die with a 6-sided on, roll the dice, and reroll on a 5 or 6.

2. I guess each roll can be simulated by a fair coin toss process interpreting the number in its binary form : )

3. Interesting theory, Bill! Another possible alternative is to call in an order at a favorite restaurant and have a lunch at home. That's what we did for mom! {Prem = a.k.a. your cousin Kim!]

4. Kim- I didn't know you read the blog!- Welcome!

This year Mom wanted to order out a pizza, so we did.
KEY- her day (even though it was a week later than the usual M-day),
her call, her pizza.

5. Talking of k-sided dies, here is a nice problem: Show that there is a 7 sided polyhedron that has the property that when rolled, it lands on each face with the same probability, namely 1/7.