all math loving people here's some interesting puzzles to solve. do attempt it once.

1.) if hospital A delivers 200 babies while hospital B delivers 1000 then can u find out which hospital has greater chance of delivering precisely as many boys as girls assuming that probability of having boy or girl is same.

2.) prove this very simple question :    1

3.) prove this inequality without multiplying whole mess out :

4.) gossip puzzle : there are six gossip loving women. whenever one of them calls another by the end of conversation they both know everything that the other knew beforehand. one day each of the six women picks up a hot gossip which are different from each other. u have to find out minimum no. of phone calls required before all six of them know all six of the gossips.

enjoy solvig these. pls post ur answer with complete solutions.

NB : these puzzles are taken from some of the books and competions where i participated.

Answer to question 2

Is the answer to the 4th question 9 phone calls?

Answer to the First question

Is it the hospital with 200 babies.

edited

Oh no I got 9 as the minimum. So either the answer is 9 or less than that (very unlikely)

i got 7 calls for the last one.

@shinee

Please check once more urs is coming 9 calls (same way that I used)

1 1 1 1 1 1     (denotes each woman knows one gossip)

2 2 1 1 1 1   

2 2 2 2 1 1      (note: woman number 1 and number 3 have 2 different gossip each)

2 2 2 2 2 2

2 2 4 2 4 2

2 6 6 2 4 2

And 4 more calls

Total 9 calls

Q4 - The answer is 8.

The 6 numbers(1,2,3,4,5,6) denote 6 ladies and A,B,C,D,E,F are 6 diff. gossips.

The no. in red at the right hand side denote the No. of calls in a particular step. And U can see that after the third step, each lady knows all 6 gossips-ABCDEF.

1A   2B   3C   4D   5E   6F

Calls- 1+2, 3+4, 5+6 = 3 calls

=> 1AB   2AB   3CD   4CD   5EF   6EF

Calls- 1+3, 4+5 = 2 calls

=> 1ABCD   2AB   3ABCD   4CDEF   5CDEF   6EF

Calls- 1+6, 2+4, 3+5 = 3 calls

=> 1ABCDEF   2ABCDEF   3ABCDEF   4ABCDEF   5ABCDEF   6ABCDEF

So, total phone calls = 3 + 2 + 3 = 8.

ans 4 the 4qus is 9 calls

let there b women  1      2      3       4     5      6

and they know gossip   a       b       c         d     e      f     rspcly

------call 1 ------1 -2

1 tells 2  abt a

2 tells 1abt b

so 1 knows  a b

2 knows ab

------call 2--------3-4

3 tells 4 abt c

4 tells 3 abt d

so3 knows  cd

4 knows cd

--------call3-------5-6

5 tells 6 abt e

6 tells 5 abt f

so  5 knows  ef

6 knows ef

----------------------------------

1 knows  abt a b

2 knows abt ab

3 knows  abt cd

4 knows abt cd

5 knows  abt ef

6 knows abt ef

------call4---1-4

1 tells 4 abt  a b

4 tells 1 abt cd

so 1 knows  a b cd

4 knows abcd

-------call5-2-5

2 tells 5 abt ab

5 tells 2 abt ef

so  2 knows ab ef

5 knows  abef

------call6-3-6-

3 tells 6 abt cd

6 tells 3 abt ef

so 3 knows  cdef

6 knows cdef

-------------------------------------------

1 knows  a b cd  (except ef)

2 knows ab ef  (except cd)

3 knows  cdef  (except ab)

4 knows abcd  (except ef)

5 knows  abef  (except cd)

6 knows cdef  (except ab)

-------call7- 1-3

1 tells 3  a b cd

3 tells 1  cdef

now

1 knows abcdef

3 knows abcdef

------call8 ---2-4

2 tells 4  abef

4 tells 2  abcd

now

2 knows abcdef

4 knows abcdef

-----call9-------5-6

5 tells 6  abef

6 tells 5  cdef

now

5 knows abcdef

6 knows abcdef

so all konw each gossip in 9 calls

ans is 9 calls

first women calls

                                   2nd 3ed 4th

second women calls

                                  3ed 4th 5th

third women calls

                  &n