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Joseph,
“Dr. Pepper: How do you know which post is what post #?”
Easy- find the post, count how many down on the page the post is, multiply the page number by 40 and add the two together.
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.
Solution to post # 292 http://www.theyeshivaworld.com/coffeeroom/topic/the-riddle-thread/page/8#post-15915
In the following equation, what Yom Tov does x equal to: 10^x = baomer?
Take logs of both sides Log(10^x) = x = Log(baomer)
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.
Here’s somewhat of a riddle for the engineers following the thread.
Why are the towers of the Verrazano-Narrows Bridge 1.625 inches further apart from each other at the tops than at the bases? (Both towers stand perfectly plumb.)
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.
squeak
This is not as innocent as it looks.
Let the original pile = y and the final pile (before it’s divided into 5) = x.
We know that x must be divisible by 4 and 5 (the last person split it into 4 even groups and the 5 people split it into 5 even groups).
y = ((((((x)*5/4+1)*5/4+1)*5/4+1)*5/4+1)*5/4+1) which simplifies to (3125*x)/1024 + (8404/1024).
(8404/1024) = 8 + 53/256 therefore the fractional part of (3125*x)/1024 must equal 203/256 (so we are not left with a fraction at the end).
=> (3125*x)/1024 = an integer (henceforth denoted as “I”) + 203/256
=> (3125*x)/1024 = I + 203/256
=> 3125*x = 1024*I + 812
So we need MOD(3125*x,1024) = 812
MOD(3125,1024) = 53
MOD(812,53) = 17
MOD(53,17) = 2
=> x = 4 * 5 * MOD(812,53) * (MOD(53,17) + 1) = 4 * 5 * 17 * 3 = 1020
=> x = 1020 and y = 3121
If we weren’t looking for the minimum value of x the correct answer would be 1020 + 1024c where c is a non-negative constant.
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.
Joseph
15,554,
7777 * 4 * 3 * 2 =186,648
186,648 / 12 = 15,554.
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.
I can only try
(X + 2 * Y = 98) minus (X + Y = 74) => Y = 24.
We are subtracting one equation from another. (Cramer’s rule would also work.)
3^2 + 4^2 = 5^2 (is that what you were thinking of?) there are an infinite more sets of three integers that will fit that relationship.
The dimples in Golf balls allow the balls to travel further by trapping air inside of them and allowing the ball to ride or “float” on the air. A more detailed explanation is beyond the scope of this thread.
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.
anon for this
(x+0.5)*(x+0.5) = x^2 +.5x + .5x +.25 = x^2 + x +.25.
=> 4.5 * 4.5 = 4^2 + 4 + .25 = 20.25
I agree that this will work but I found that my students had a hard time performing more than two mathematical operations mentally. (x+0.5)*(x+0.5) = x^2 +.5x + .5x +.25 reduces to three terms x^2 + x +.25 , by (x – 2)*(x + 2), the two middle terms cancel out so there are only two terms left, x^2 – 4.
If you (or your daughter) have no issue with this consider yourself gifted.
Mrs. “anon for this”,
Here’s how it works,
Instead of x and x + 2, let’s use (x – 1) and (x + 1). Now FOIL (Firsts, Outers, Inners and Lasts) gives us (x – 1)*(x + 1) = x^2 + x – x – 1^2 = x^2 -1.
So 6 x 8 = (7 – 1)*(7 + 1) = 7^2 – 1 = 48.
This will also work for (x – 2)*(x + 2) = x^2 – 4 and so on.
Here’s a trick I figured out for squaring an integer where the units digit is 5. Let’s square 75. Take all the digits besides for the last one (in this case it’s just the number 7) multiply it by by that number + 1 (7 * 8 = 56) and attach the numbers 25 at the end (5625). Please check that 75 * 75 = 5625.
Proof (10x + 5)^2 = 100x^2 + 50x + 50x + 25 = 100x^2 + 100x + 25 = 100(x^2 + x) + 25 = 100 * x * (x + 1) + 25.
Now try it for 45 and move the decimal two spots to the left for 4.5 ^ 2. You should get 20.25.
Joseph,
-40 degrees Celsius = -40 degrees Fahrenheit
I think the North Pole would be one place.
Joseph,
Let X = humans and Y = Horses
X + Y = 74
2 * X + 4 * Y = 196 => X + 2 * Y = 98 (divide both sides by 2)
(X + 2 * Y = 98)
-(X + Y = 74)
=> Y = 24 => X = 50
50 Humans and 24 Horses.
I can only try
I actually thought I got it after the first line but I was wrong.
I did 1 x 5 x 8 x 1 x 2 = 80.
But no!
Next I found the prime factorizations and got almost nowhere on the first line (except that I found many instances of the number 2) but on the second line there was one 7 on the left side and two on the right so I knew that one of the terms was squared.
The rest was smooth sailing.
Here’s an old one:
In the following equation, what Yom Tov does x equal to: 10^x = baomer?
(It was taken from the secular riddle 10^x = cabin.)
I can only try
Why the extra steps?
This is how I would do it:
15, 8, 12, 80 ==> 15 x 8^2 / 12 = 80
18, 7, 6, 147 ==> 18 x 7^2 / 6 = 147
19, 6, 12, ? ==> 19 x 6^2 / 12 = 57
Nobody
If there’s something you don’t understand please ask. I’m here to help. I understand that it may be hard to follow because of the formatting but I wouldn’t consider this example challenging.
I can only try
0 = 2*0*0*9
1 = 2^0+0*9
2 = 2+0*0*9
3 = 2*0*0+?9
4 = 2^0+0+?9
5 = 2+0+0+?9
6 = (2+0+0)*?9
7 = -2+0+0+9
8 = -(2^0)+0+9
9 = 2*0*0+9
10 = 2^0+0+9
I probably should have defined some terms.
A matrix is a rectangular array (m by n) of numbers. It can be a single number (a 1 by 1 matrix) or any other dimension (m and n must be positive integers). A matrix is denoted by brackets on both sides.
A determinant is a value only given to a square matrix (where m = n). For a 1 by 1 matrix the determinant is the lone entry. For a 2 by 2 matrix
a b
c d
the determinant is (a)*(d)-(c)*(b).
The formula for a 3 by 3 matrix was mentioned above in my previous post.
Please don’t ask me to post the formulas for anything greater than m = n = 3, they are very long.
The determinant of a matrix is denoted by vertical bars on both sides. For example if we have a matrix named “A” then the determinant of “A” is denoted by |A|. There are also text books that put the vertical bars on both sides of the whole array to denote the determinant.
I apologize if I offended anyone, with out even thinking I put a title of Reb out of respect for my fellow Yidden, but I’ll stop.
“I can only try”
In the future feel free to ask any math questions, and please don’t think you are taking advantage- I’m here to help.
Here’s how the rule works, (if you know of anyway that I can attach a PDF file to a post or somehow upload a file somewhere that I can link here please let me know. This is hard to follow without mathematical formatting).
2x + y + z = 3
x + 2y + z = 0
Given the general form of a system of three linear equations with three unknown variables:
ax + by +cz = j,
da + ey + fz = k,
ga + hy + iz = l
put this in matrix form:
a b c
d e f
g h i
(3 x 3 matrix)
multiplied by
x
y
z
(3 x 1 matrix)
equals
j
k
l
(3 x 1 matrix)
x =
the determinant of:
j b c
k e f
l h i
divided by
the determinant of:
a b c
d e f
g h i
(The determinant of a 3 x 3 matrix
a b c
d e f
g h i
For our example:
a = 2, b = 1, c = 1, j = 3
d = 1, e = -1, f = -1, k = 0
g = 1, h = 2, i = 1, l = 0
therefore the determinant of
j b c
k e f
l h i
is the determinant of
3 1 1
0 -1 -1
0 2 1
= 3
the determinant of
a b c
d e f
g h i
is the determinant of
2 1 1
1 -1 -1
1 2 1
= -2 -1 + 2 +1 +4 -1
= 3
therefore x = 3/3 = 1.
Similarly
y =
the determinant of:
a j c
d k f
g l i
divided by
the determinant of:
a b c
d e f
g h i
and
z =
the determinant of:
a b j
d e k
g h l
divided by
the determinant of:
a b c
d e f
g h i
The final results are x = 1, y = -2 and z = 3.
I hope this helps.
Reb “anon for this”,
I never looked at it that way, but I guess it would be easier to program a computer to calculate the unknown variables as the ratio of two determinants than to pivot the equations using the Gaussian elimination method.
At first I also assumed that Cramer was the Vilna Goan. When I asked someone in yeshiva if “Cramer was the Vilna Goan”? He looked at me like I was on Coke and said “From Seinfeld”? (From then on I remembered that Gabriel Cramer spells his name with a C.)
This sounds like Cramer’s rule. It is very efficient for solving systems of differential equations, but I guess it could be used for linear equations (although there are easier methods that do not require computing the determinant).
In any case the rule is named after Gabriel Cramer who lived at the same time as the Vilna Goan, but was a different person.
I can only try
Dr. Pepper-
Pick the one that you like best (if any):
1) Sorry Dr., but that answer grades “incomplete”
2) Now say that ten times fast
3) I’m NOT chipping in to replace your worn-out keyboard
4) I think the eleventh zero on line 5071 should be a nine. Please double check.
5) Anybody could’ve done that. Let’s see you say it backwards.
6) This actually makes more sense than most extra-long posts.
7) YWN’s server now needs a new batch of 0’s and 1’s delivered.
(Did you ever read “The Code Book”? I think you’d enjoy it.)
I’ll pick number six.
What I like about this thread is the amount of respect everyone has for each other and there is no fighting. Can anyone else think of another topic where we can schmooze like human beings? The moderators would like it.
noitallmr
Dr. Pepper- Your a genius!
Have you ever taken an I.Q test?????
Thanks for the compliment! But most of the stuff I posted is high school level.
Hi Everyone,
The swelling in my fingers from my post on Sunday finally went away and I can type again.
Getting back to that riddle with the teacher- when I was in 10th grade we were learning ???? ????? and in ??? ?? the end of second Mishna says ?????? ???? ?? ???????, ????? ???? ?? ??????–???? ???? ?? ????? ??????; ??? ????, ???? ????? ?? ??????? ???? ??? ?????. So our Rebbe asked us to add up the total amount of 1 + 2 + 3 + … + 60.
The plan I came up with was to add the numbers 1 through 10 (I used a shortcut for this, I already knew from the boxes of Chanukah candles that Telze sends out that the sum of the integers of 2 through 9 is 44 and 44 + 1 + 10 = 55), the sum from 11 to 20 is just 100 more and from 21 to 30 is just 100 more than that. Continuing we have 55 + 155 + 255 + 355 + 455 + 555 = 50 + 150 + 250 + 350 + 450 + 550 + 6×5 = 1800 + 30 = 1830.
It’s not as fast as the other one I posted and is impractical for large numbers and numbers not ending in 0, but it does work.
1) What was the answer?
2) What was the student’s “trick”?
3) Who was the student?
1) 5,050
2) There are 100 integers, 1 through 100. Add the first and last => 1 + 100 = 101. Add the second and second to last => 2 + 99 = 101. Continue the process until the fiftieth and fiftieth to last => 50 + 51 = 101. Therefore we have 50 pairs of 101. 50 x 101 = 5,050. In general to add the integers 1 through n the formula is (n/2)*(n+1) or more commonly written as (n*(n+1))/2. (This works for all n where n can be odd or even.)
3) If I remember correctly the student was Carl Friedrich Gauss who lived in the late 1700s to mid 1800s.
Good night everyone
3.
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2722697504 31873
7
6 x 7 = 42 & 4+2 = 6
3 x 9 = 27 & 2+7 = 9
4 x 5 = 20 & 2+0 = 2
8 x 2 = 16 & 1+6 = 7
Sorry about the formatting in post # 193, I tried leaving spaces so that it would look like two columns but I don’t know where they went. I’m going to put semicolons in this time.
If the number is in the following range; The first digit is
0 to 1,000; 0
1,000 to 8,000; 1
8,000 to 27,000; 2
27,000 to 64,000; 3
64,000 to 125,000; 4
125,000 to 216,000; 5
216,000 to 343,000; 6
343,000 to 512,000; 7
512,000 to 729,000; 8
729,000 to 1,000,000; 9
If the number ends in; The second digit is
0; 0
1; 1
2; 8
3; 7
4; 4
5; 5
6; 6
7; 3
8; 2
9; 9
I hope this makes the process easier to understand.
I wouldn’t call this a riddle (it’s more like a trick) but some of you may find it as interesting as some of my students did. (This is how I’d bribe them to behave. If, for example, they would go a whole week without anyone making a silly reference to a popular soft drink with the same name, then I’d show them a trick.)
Have someone pick a two digit number and cube it (let’s pick 58; 58 x 58 x 58 = 195,112). Now they tell you what the result is and you calculate the cube root in your head and tell them the original number.
Here’s how to do it:
If the number is in the following range The first digit is
0 to 1,000 0
1,000 to 8,000 1
8,000 to 27,000 2
27,000 to 64,000 3
64,000 to 125,000 4
125,000 to 216,000 5
216,000 to 343,000 6
343,000 to 512,000 7
512,000 to 729,000 8
729,000 to 1,000,000 9
If the number ends in The second digit is
0 0
1 1
2 8
3 7
4 4
5 5
6 6
7 3
8 2
9 9
Getting back to our example- 195,112 is in the range 125,000 to 216,000 => the first digit is 5 and 195,112 ends with a 2 => the second digit is 8 and we get our original number 58.
Disclaimer- I wouldn’t advise performing this trick on a first date, but if you must- be sure to bring a calculator. Most of the girls I dated couldn’t even square a two digit number in their head, let alone cube a number.
You all have a Gut Shabbos now.
ABCDE x 4 = EDCBA
ABCDE < 25,000 or ABCDE x 4 would be greater than 99,999 => A = 1 or 2.
If A = 1 then 1BCDE x 4 = EDCB1, this would mean that the units digit in the product of E x 4 is 1, but the units digit of the product of an even number and any other integer must be even => A <> 1 so A = 2.
We now have 2BCDE x 4 = EDCB2.
The units digit of E x 4 must eqaul 2 => E = 3 or 8. E can not = 3 since 2BCDE x 4 > 80,000 so E must be either 8 or 9 => E = 8.
We now have 2BCD8 x 4 = 8DCB2.
B can be only 1. (B Can’t be 2 since A already is and if B is 3 than 23CD8 x 4 will be greater than 90,000 and we already determined that E = 8.)
We now have 21CD8 x 4 = 8DC12.
D can only be 2 or 7 since the product ends in 12 => D8 x 4 ends in 12 (which is only acheived with 2 or 7) and since A = 2 => D = 7.
We now have 21C78 x 4 = 87C12.
The fastest way to get C is probably by trial and error.
C happens to be 9.
21978 x 4 = 87912
This is just my humble opinion, but every person interested in getting married should be looking for the person who they would like to spend the rest of their life with and who they would like to work together with to bring up children in the way that Hashem wants them to.
It can be frustrating at times, but just be yourself. Hashem created you with love and Hashem created someone else (also with love) just for you.
May you all merit to find your spouse in the proper time.
Good Morning Reb “I can only try”,
It’s scary what others can deduce just by looking at the choice of words one uses in a seemingly innocent paragraph!
Here’s another riddle that can be solved both mathematically and visually:
Let’s say that you are playing a game with a friend and you are shown three curtains. Behind one of the curtains is a prize, and there is nothing behind the other two. To win the prize, you simply have to choose which curtain it is behind. When you choose a curtain, your friend opens one of the curtains you have not chosen, and shows you that there is nothing behind it. You are then given a choice; you may stick with your original choice, or you may switch to the remaining closed curtain.
Will your chances of winning increase or stay the same if you now choose the other curtain?
Reb “I can only try”,
I saw this somewhere before (possibly when I took the SATs…).
Here’s how I did it-
40 MPH = (2/3) MPM (Miles Per Minute)
30 MPH = (1/2) MPM
=> x*(2/3) = (60-x)*(1/2) => x = 180/7 = 25.71429 and (60-x) = 34.28571.
The weighted average is (25.71429/60)*40 + (34.28571/60)*30 = 34.28571, which was choice A.
How did you know I was a teacher? Were you a student of mine? I was actually a teacher while I was going for my Ph.D (hence the Dr. title) but no longer teach.
If you like these math riddles let me know, I’ve got some more of them which might be too technical for most people reading this thread.
Also I was just kidding about the answer being A, I don’t remember the choices.
61,52,63,?,46
I think the pattern starts earlier, 1,4,9,61,52,63,94,46,18,001,121,441,961,691,522…
But thanks,
I really enjoyed that one.
I wouldn’t want to put myself in a situation like Reb Azi did, but if I would see some one with a hat, jacket, tie and beard standing outside I would definitely not suspect him of having anything less than the best intentions.
Thank you Reb Azi.
Yes, Reb anon for this, that is correct.
Here’s one from the textbook I used for calculus;
A hiker takes his time walking slowly and making many stops along a trail from 7:00 A.M. to 7:00 P.M. where he rests for the night. The next morning at 7:00 A.M. he begins his leisurely walk back along the exact same route, again making many stops along the way (not necessarily in the same places), and finishing at 7:00 P.M.
Is there for certain a place along the route where he was in that exact spot the same time on both days? The question isn’t asking where the particular spot is, only if such a particular spot exists.
(Hint: The answer book wanted required a minimal knowledge of function graphing, however this can be answered with no math background.)
Reb Head,
I’m very sorry to hear about the summons. It would be a shame to have to pay so much money that could otherwise be used for better purposes.
I suggest that you look the summons over very carefully noting even the slightest mistake, but regardless of the accuracy you should try to dispute the summons. The Department of Finance may offer to remove one third of the fine if you plead guilty.
Please have a look at the “Alternate Side Parking Rules Suspension Calendar” http://www.nyc.gov/html/dot/downloads/pdf/asp2008.pdf and note that “Double parking of passenger vehicles is illegal at all times,
including street cleaning days, regardless of location, purpose
or duration”.
Good Luck!
There are those who say that Yidden are better because we were born that way and there are those who say that we are better because we make ourselves better.
I’d rather not take any side, but how about everyone give one idea how we could make ourselves stand out as role models for the rest of society.
When I take my kids for a walk; if we see a cop sitting in a car I tell my kids to wave. The cops usually smile and wave back. At times they even turn on their light to make the little ones laugh. There’s at least one cop who patrols our neighborhood who recognizes my kids and will wave to them if he notices them first.
Although this hasn’t happened yet but I think that if I returned to our car and was about to get a ticket (for an expired meter or something similar) from a cop who in the past noticed that we took the time to say hello, I would have a high probability of getting a second chance.
When I take the bus or train I always make sure to thank the driver and conductor. (These people hold positions where they are part of the scenery and usually only get noticed when something negative occurs. They appreciate when others acknowledge that they exist and show them some gratitude for their hard work.)
Finally, when I call a customer service and get greeted by “May I have your name and address/ account number …?” I always say, “Hi, How has your day been so far?” they always say something like “good, thanks for asking, how about you?” and then the operator is usually more relaxed and easier to deal with. (This might not be a Kiddush Hashem per se, after all how many representatives out there who never met a Yid would know that Pepper is a Yiddish name?)
Thanks everyone and hopefully after we all accept the wonderful ideas that others are going to suggest we will merit seeing the redemption in our days and then the whole world will know why Yidden are the best!
Reb somebody and Reb jphone,
You’re correct, I did not mean to write that. I didn’t realize I wrote it until I submitted the reply and I could figure out how to edit the post.
I assure you that I pray to the one above and no human being.
One night after Maariv some neighbors and I passed a young Chasideshe couple stuck on the side of the road with a flat tire. From the way they were dressed it was obvious that they were on the way to a wedding.
Setting our personal views aside, (we may have different views but at the end of the day we all pray to the same person,) we offered to change his tire for him so that he wouldn’t have to walk into the wedding with dirty hands and full of sweat.
While some of us were changing the tire, others were giving him directions to 24 hour tire repair shops in the surrounding neighborhoods while others waited just to make sure they were able to drive off safely.
After the change was done he asked for our names and asked us to take his name so he can repay us if we ever need help in his neighborhood. We all refused saying that we didn’t want him to feel as if he owed us anything.
He and his wife thanked us over and over again, then they got into the car, he rolled down his window and said, “Mi K’amcha Yisroel”, and drove off.
I think I should mention at this time that while some of the biggest Mitzvos are done anonymously, unfortunately the opposite is also true by aveiros.
Please my dear friends, before posting a vicious attack against anyone online, wait a few seconds and think if you would use the same wording if you had to sign your real name.