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This thread is dedicated for posing mathematical challenges.
Here are a few to start off:
1.
Avrumi and Baruch just became friends with Chaim, and they want to know when his birthday is. Chaim gives them a list of 10 possible dates:
<br />
May 15 16 19<br />
June 17 18<br />
July 14 16<br />
August 14 15 17<br />Chaim then tells Avrumi and Baruch separately the month and the day of his birthday respectively.
Avrumi : I don’t know when Chaim’s birthday is, but I know that Baruch doesn’t know too.
Baruch: At first I don’t know when Chaim’s birthday is, but I know now.
Avrumi: Then I also know when Chaim’s birthday is.
So when is Chaim’s birthday?”
2.
Multiple Choice:
3.
Express ?48 in the form n?3, where n is an integer.
4.
5.
How many 4-digit numbers are there such that the thousands digit is equal to the sum of the other three digits?
Details and assumptions:
The number 12 = 012 is a 2-digit number, not a 3-digit number.
Are you sure this isn’t someone’s homework?!! I recall having similar questions on math assignments in eleventh grade…
good for Joseph, the way it was originally writtn was incredibly un-tznius. What buisness do Albert and Bernard have becoming friends with Cheryl?
Though it pains me that Jospeh didnt change the goyish dates
1. My brain is too tired
2. a.
3. sorry don’t know how to do fancy formatting 48^(1/2)=16*(3^(1/2))
4. b. not overly familiar with parametric equations but if you are asking for dx/dt i am assuming you differentiate the function containing those variables
5. Literally??????
How did I do?
July 16th I think. I forgot to write it down and now I have to start all over.
sorry, my head does not process in english. i doubt there is more than one way to arrive at the correct answer (without cheating) and i didn’t cheat.
that’s the best explanation i can give right now.
I meant something more along the lines of neural synapses.
I know it’s in July or August, b/c if it was in May or June, Baruch could have heard 19 or 18 and known which month and Avrumi couldn’t have said that Baruch doesn’t know for sure. But I don’t know more than that
Thank you Joseph for that great riddle. It took me some time to work it out, but I think I have it.
The correct date is 16 July.
Here is my thought process:
It couldn’t have been May, as then there would have been the possibility of Baruch knowing the birthday, namely if Chaim would have said 19, which is a date which only appeared in May.
For the same reason it couldn’t have been June, as then there would have been the possibility that Baruch was told 18, which only appeared in the June list.
This is as far as Avrumi could have known at this stage.
However by him saying so, Baruch now knew that May & June were out. But it could still have been July or August.
Now, if he would have been told 14, he still couldn’t know the correct month, as that appears in July & August. Therefore if he was told 16, he knew it was 16 July; if he was told 15 or 17 he knew it must be August. So he now knew the correct date.
Because of Baruch’s statement, Avrumi now also knew that 14 July was out.
If Avrumi would have been told “August”, he still wouldn’t have known which day in August. From the fact that he claimed to know, he must have been told “July” and the birthday must have been 16 July. Mazzel Tov!
The asnwer to question 3 is 4?3, as ?48 = ?3×16 = 4?3
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