# Mathematical Challenges

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• #616284
Joseph
Participant

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.

#1098393
Joseph
Participant

The dates in Question 1 didn’t format very well. Here they are, again:

``` May 15 16 19 June 17 18 July 14 16 August 14 15 17 ```

#1098395

Are you sure this isn’t someone’s homework?!! I recall having similar questions on math assignments in eleventh grade…

#1098396
Joseph
Participant

Then you should have no trouble at all easily answering this stuff (without cheating, of course). Nu, let’s hear some numbers.

#1098398
ubiquitin
Participant

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

#1098401
profound101
Participant

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?

#1098402
Joseph
Participant

2. Correct!

3. That’s not the answer to the question.

4. Correct!

Multiply by the power (in this case 8 x -2 = -16).

Is anyone going to try to answer #1?

#1098403
🍫Syag Lchochma
Participant

July 16th I think. I forgot to write it down and now I have to start all over.

#1098404
Joseph
Participant

#1098405
🍫Syag Lchochma
Participant

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.

#1098406
Joseph
Participant

sorry, my head does not process in english.

We’ll consider an answer if it has an explanation in Yiddish or Hebrew as well. 😉

#1098407
🍫Syag Lchochma
Participant

I meant something more along the lines of neural synapses.

#1098408
Yid0018
Member

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

#1098409
Imanonov
Participant

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!

#1098410
Imanonov
Participant

The asnwer to question 3 is 4?3, as ?48 = ?3×16 = 4?3

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