Dr. Pepper

You have a rectangular pan of cake and someone cut out a random square somewhere on the cake (not in the middle).

Using one cut how can you split the cake exactly in half?

I can only try-

I hope this comes out looking decent.

# => Number of Hearts left in the deck.

# of ways => Number of way that that amount of Hearts can be chosen from the 32 that are removed.

Prob => Probability of picking a Heart from the 20 left.

(This is done using Excel)

# # of ways Prob. # of ways * Probability

0 15,380,937 0.65 0.0000000793494867

1 799,808,724 0.6 0.0000038087753615

2 16,529,380,296 0.55 0.0000721551332366

3 181,823,183,256 0.5 0.0007215513323662

4 1,198,380,071,460 0.45 0.0042801113124451

5 5,033,196,300,132 0.4 0.0159790822331284

6 13,938,082,061,904 0.35 0.0387185454110420

7 25,885,009,543,536 0.3 0.0616336028992096

8 32,356,261,929,420 0.25 0.0642016696866767

9 26,963,551,607,850 0.2 0.0428011131244512

10 14,592,039,693,660 0.15 0.0173722165034537

11 4,864,013,231,220 0.1 0.0038604925563231

12 896,002,437,330 0.05 0.0003555716828192

13 68,923,264,410 0 –

Total 125,994,627,894,135 0.2500000000000000

Here are the formulas used: (Starting from Cell A1)

# # of ways Probability # of ways * Probability

0 =COMBIN(13,13-A2)*COMBIN(39,7+A2) =(13-A2)/20 =(B2/$B$16)*C2

1 =COMBIN(13,13-A3)*COMBIN(39,7+A3) =(13-A3)/20 =(B3/$B$16)*C3

2 =COMBIN(13,13-A4)*COMBIN(39,7+A4) =(13-A4)/20 =(B4/$B$16)*C4

3 =COMBIN(13,13-A5)*COMBIN(39,7+A5) =(13-A5)/20 =(B5/$B$16)*C5

4 =COMBIN(13,13-A6)*COMBIN(39,7+A6) =(13-A6)/20 =(B6/$B$16)*C6

5 =COMBIN(13,13-A7)*COMBIN(39,7+A7) =(13-A7)/20 =(B7/$B$16)*C7

6 =COMBIN(13,13-A8)*COMBIN(39,7+A8) =(13-A8)/20 =(B8/$B$16)*C8

7 =COMBIN(13,13-A9)*COMBIN(39,7+A9) =(13-A9)/20 =(B9/$B$16)*C9

8 =COMBIN(13,13-A10)*COMBIN(39,7+A10) =(13-A10)/20 =(B10/$B$16)*C10

9 =COMBIN(13,13-A11)*COMBIN(39,7+A11) =(13-A11)/20 =(B11/$B$16)*C11

10 =COMBIN(13,13-A12)*COMBIN(39,7+A12) =(13-A12)/20 =(B12/$B$16)*C12

11 =COMBIN(13,13-A13)*COMBIN(39,7+A13) =(13-A13)/20 =(B13/$B$16)*C13

12 =COMBIN(13,13-A14)*COMBIN(39,7+A14) =(13-A14)/20 =(B14/$B$16)*C14

13 =COMBIN(13,13-A15)*COMBIN(39,7+A15) =(13-A15)/20 =(B15/$B$16)*C15

14 =SUM(B2:B15) =SUM(D2:D15)

Joseph-

He was not a Kohein, nor was he divorced. He only said it to be excused from dating her.

I did not believe the story at first until he said who the Shadchan was.

22OldGold-

There was a story about 8 – 10 years ago about a step- brother and step- sister (I think from Monsey) who married each other, but I don’t think there was a shadchan involved.

The Big One

I can only try

Getting back to your posts from two weeks ago, my wife was teasing me that if I keep pulling my pants up higher and higher while my sense of humor keeps getting worse and worse that people will start thinking I’m a grandfather. Then she saw those posts and couldn’t stop laughing.

This baby is our fourth Bli Ayin Hara.

By the way- her older siblings are crazy over her.

There was one subliminal message hidden in the post though.

When my previous child, a son, was born I had told a friend that I had a “baby”. He spread the word that we had a girl. He later said that when one has a boy they say that they had a boy, but when one has a girl they say that they had a baby.

I was curious to see if anyone would pick up that I didn’t specify the gender and figure out that we had a girl.

Joseph-

I think AXA Equitable refers to that product as YRT, Yearly Renewable Term.

But what do I know? I’m just the 800 lb. gorilla in the room.

areivimzehlazeh- Was that meant for “The Riddle Thread…”?

kapusta, outoftowner, oomis1105- I left out details which I felt were not important.

She did not do any research on this person before she went out with him. Her intentions were to do the research after the first date if there was a possibility of a second date which she eventually felt there was not. I don’t think it’s far fetched that after one year the only memory of him was a diary entry.

As far as her parents are concerned- she is one of the youngest of a large family and when the name came up they thought it sounded familiar but weren’t sure if it was a mere suggestion for her or any of her older sisters, or if any of them actually went out with him (they don’t keep records).

I doubt she’s the only one that keeps notes about her dates, I’ve heard of others who also do. (I personally never did.)

The girl happens to still be single but I have no idea about the guy.

Any other questions?

This happened to the sister of someone I went out with.

So the guy and girl are out on a date and quickly run out of things to talk about. They get up to walk around and he asks her if she was ever here before. She remembers being brought there a year before by a guy but couldn’t remember any details. He said he once brought a girl there but couldn’t remember who.

Eventually they realized that they had gone out with each other the previous year and to the same exact place. They spent the rest of the date trying to remember who said no. (They couldn’t figure it out until she got home and checked her notes, buy at least they had something to talk about.)

Sadly it didn’t work out. Maybe the third time around it will.

Some posters have written that they are reluctant to share some funny stories since then they will reveal their identity.

Please, we all like a good laugh, just say it happened to someone you know.

Here’s one that happened to someone I know (it really wasn’t me).

This friend of mine borrowed his brothers car for the date and his brother warned him that if anything happens to the car, even if it’s not his fault, he’s in big trouble. When he was returning to the car after the date he thought he saw a few teenagers opening the doors and getting in. He started running and screaming, “don’t you dear touch my car”. The boys backed off terrified until he realized that his brothers car was a few cars ahead.

He then went back to the bewildered girl and apologized. She said it was O.K. and now she has a funny story to tell her friends.

SJSinNYC

A similar story happened to two friends of mine when we were in yeshiva in Israel.

Both were Dovid and both had dates on the same night through the same shadchan.

I’ll never understand why, but the shadchan set up both dates to meet at the same place in the same hotel. A few minutes in one Dovid realized he was dating the wrong person and went to find the other Dovid (and his date) so they could switch.

Another similar story- one shadchan thought she had a great idea for a guy I knew from yeshiva and wanted to speak it over with another shadchan before she suggested it. The second shadchan thought she was talking about another guy and decided to call him and suggest it before the first one did (since it was such a good idea). The second guy ended up getting engaged to her.

The Big One-

My wife can’t stop laughing at your post. What did I say that made you think I am older than I really am?

I can only try

That’s correct, no matter how many cards are removed (up to 51 and assumning that it is not known which cards are removed) the probability of the picking a heart will be 1/4. Let’s see you prove it for where 32 cards are removed.

(Hint- there are 125,994,627,894,135 different ways that 32 cards can be chosen from a deck of 52 where order doesn’t make a difference. Hope this helps!)

Yes ames you are correct, the answer is 1/4.

Here’s how I solved the problem when I had it on an exam.

There are 1,326 unique ways to choose 2 cards from a standard 52 card deck. (52 x 51 / 2 = 1,326. We divide by two since order doesn’t matter i.e. a seven of spades and a king of clubs is the same group as a king of clubs and seven of spades.)

Of the 1,326 possibilities 78 include 2 hearts (13 * 12 / 2= 78), 507 include one heart and one non-heart ( 2 * (13 * 39 / 2) = 507) and 741 consist of two non-hearts (39 * 38 / 2 = 741). (Please note that 78 + 507 + 741 = 1,326.)

If two hearts are missing from the deck the probability of picking a heart is 11/50.

If one heart is missing from the deck the probability of picking a heart is 12/50.

If no hearts are missing from the deck the probability of picking a heart is 13/50.

So the probability of two hearts missing (78/1,326) x the probability of picking a heart (11/50) = (78/1,326)*(11/50).

Summing up the probabilities from all three scenarios gives us (78/1,326)*(11/50) + (507/1,326)*(12/50) + (741/1,326)*(13/50) = 1/4.

gleeg-

The distance traveled can not be a negative number. If the question was how much higher is the ball when it stops bouncing then -8 would be correct.

While I was driving back this really nice girl after a date I thought I was going through a yellow light and only realized it must have been red when the flash from the camera lit up the night. I tried to disregard it but she said, “Don’t worry, just send me a copy of the picture and I’ll pay for half of it”. (It never came.)

On a subsequent date we were walking in a park and stopped by an observation point to look at the scenery. Out of the corner of my eye I saw some blond hair walking away and, assuming it was her, started walking next to her. When I started to make conversation about the scenery she said something that the moderators wouldn’t approve of (it had something to do with her lineage). I looked down and it was not her. It was so embarrassing.

I returned to the lookout and there she was standing next to another guy (who was also about 12 inches taller than her and wearing a black suit jacket) telling him about a different time she was in the area. You should have seen the look on her face when she saw me and realized that she was talking to someone else. She apologized and said that, due to the difference in height, when she stood next to me she could only see my arm and shoulder. I assured her not to worry since it could happen to anyone. (I never told her what happened to me just one minute earlier.)

I got this idea from a friend of mine (he eventually married the girl he was dating at the time), I started talking in a monotone for 30 minutes about the history of the theorem, the different conjectures used to prove the theorem as well as using my fingers to draw the 3D graphs used to prove the theorem (in the hotel lobby). I still crack up when I think about the scene- some guy in a hat, jacket and tie using both his hands to plot x, y and z points on an imaginary 3D grid, while the girl sitting across from him is nodding reassuringly that she understands everything he is saying.

I couldn’t argue with that.

moish01- The soda with the same name as me is Dr Pepper (not Dr. since it’s not a real doctor), I hope this removes any confusion.

teen- The problem says “What is the total vertical distance the ball will eventually travel?” not “What is the total vertical distance traveled by the ball when it comes to a complete stop?”. The ball will never come to a complete stop but the vertical distance travelled will eventually reach a limit as the amount of time elapsed approaches infinity, what is this limit?

The answer is 56 feet.

I can only try- 24 feet is the upward distance, multiply that by two for the distance it travelled down each time it bounced up plus the original 8 foot drop gives the correct answer of 56 feet.

A boy drops a rubber ball from a height of 8 feet above a concrete floor. Each time the ball hits the ground it bounces up 75% of its previous maximum height (it reaches 6 feet on its first bounce, 4.5 feet on the second bounce…). What is the total vertical distance the ball will eventually travel?

Put them together like a “T”. The middle of a bar magnet will not be magnetized because the magnetic force from the poles are cancelled out in the middle. If they are attracted to each other then the vertical bar is the magnet. If there is no attraction then the horizontal bar is the magnet.

Hi everyone,

It’s great to be back, I missed you all!

Here’s a riddle for today:

What’s red and white, 19.5 inches long, weighs 7 lbs. 6 3/4 oz, cries a lot and gives Dr. and Dr. Pepper so much nachas?

I can only try-

“Dr. Pepper – don’t be modest now, because I’m really curious – is this level of math expertise common among math majors? Among holders of a math PhD?”

I hate questions like this because I don’t want to appear arrogant. The math used to solve that riddle was basic algebra and arithmetic (the MOD(x,y) function is just a fancy way of getting the remainder of x divided by y).

Let me try to explain the thought process of a mathematician the way I heard it from the son of a math professor (it’s not supposed to be funny so don’t complain that you find it corny):

Q. What do you do if you see a piece of wood on fire and a pail of water next to it?

A. Use the pail of water to put out the fire.

Q. What do you do if you see a piece of wood on fire and there is no pail of water next to it?

A. Go get a pail of water and put out the fire.

Q. What do you do if you have a pail of water?

A. Go find a piece of wood to set on fire so you can pour the bucket of water on it.

The way a mathematician goes about solving a problem is to take it apart and change it around to fit into an equation he knows how to handle.

By the time a math major gets to upper level math courses, even calculus should come naturally. When they are trying to set up a mathematical model to solve some sort of equation on an exam they don’t have time to try to figure out how to differentiate or integrate the equation.

squeak

brute force method using Excel: (only copy and paste what is between the quotation marks)

Cell A1 “1”, Cell B1 “=((((((A1)*5/4+1)*5/4+1)*5/4+1)*5/4+1)*5/4+1)”, Cell C1 “=B1-INT(B1)”

Select Cells A1 – A3 and move the cursor to the bottom right hand corner of Cell C1 until it turns into a + sign. Now click on the + sign and drag the formulas down a few thousand rows.

Select column “C” and on the “Standard” toolbar click “Sort Ascending” (The icon has an A on top of a Z with a down arrow on the right side). Select to “Expand the Selection” and click “Sort”. The rows where the entry in column C is 0 are possible solutions.

squeak

This brings back memories from when I first solved this problem on my abacus… If you read post # 203 http://www.theyeshivaworld.com/coffeeroom/topic/the-riddle-thread/page/6#post-12885 in this thread you’ll understand how I remember the question.

Anyway- what’s “clam stuff”?

And by the way- I am not that old, I was born after the 50s.

Joseph,

I read the question too fast too late at night. I thought it said that half was remaining, then one third was remaining, then one quarter was remaining…

I can only try

Andrew Wiles announced a proof in 1993 which was almost complete but a colleague of his, I think his last name is Katz, found a “hole” in the proof. Andrew Wiles spent about another year with one of his students “plugging the hole” and I far as I know the proof has been accepted.

This might be a legend but I heard that in the 1800s and early 1900s there were large rewards set aside for the first one to prove (or disprove) the theorem. Unfortunately for Wiles the rewards were in German Marks held in German banks and after the record inflation Germany suffered after World War I, the rewards were practically worthless.

I can only try

There are actually an infinite amount of integers that will satisfy the equation a^2 + b^2 = c^2, another common example is 5, 12 & 13. There are no integers for a, b, c and n such that a^n + b^n = c^n for n > 2. (Please don’t ask me to prove Fermat’s Last Theorem here.)

Of the many uses of Pythagorean Triples, as they are called, the most common one is finding the length of the hypotenuse of a right triangle given the length of the legs. If the legs measure 3 and 4 respectively then the hypotenuse will measure 5.

Here’s another one from an upper level math course (that can be answered in English with basic mathematics skills):

Does there exist a prime number “P” such that there is no prime number greater than “P”? (Is there a highest prime number?)

If “P” exists what is it, if not why does “P” not exist?

SJSinNYC

My Ph.D. is not in engineering but I did take some engineering courses. If you have some questions I’ll be happy to try to help you.