Post mathematic related questions here

OP
rst

rst

Youngling
Re: mathematic related questions

solving maths question is really a fun (if you get right answer)
 
Niilesh

Niilesh

Padawan
Re: mathematic related questions

rst said:
I think Its only possible with "hit and trial" method
If not, plz explain
Click to expand...
If the answer would have been two or three digit maybe i could have solved(without hit and trial) it but the answer is in 6 digits!


If anyone can explain whats written here it would be appreciated(its the solution)
After thinking about the problem for a couple of minutes (kinda embarrassed it took that long to get it), I went directly to the answer, no trial and error. Further, I can also tell you that the next lowest number with this property is 571428 and that there are no other numbers less than 10^50 with this property.

What I realized is that I needed to find a repeating fraction such that the number of repeating digits was one less than the number. This would be a prime number, and seven is the lowest number with this property. With this property, every digit in the repeating fraction appears in each place exactly once (i.e. every repeated digit appears as the first digit after the decimal exactly once for n/p where p > n > 0).

Now I wanted to find any occurances where the nth digit followed the 1.5nth digit.

The repeating digits in 1/7 and their corresponding 'n' where the digits are the first digit after the decimal point are:

142857 - repeating digits
132645 - n

n=2 follows n=3, so the lowest number is 285714. Also, n=4 follows n=6, so the next number is 571428.

Out of curiosity, I checked all the prime numbers up to 50. The ones with p-1 repeating digits are:

17, 19, 23, 29, 31, 47

None of these has two adjacent digits with the desired property, so there is no other solution with less than 50 digits.

I'd be curious if there was a way to either prove that no other solutions exist, or determine which prime numbers would have the required relationship. I think other solutions do exist, but I'll write a program to check them any furthur.
Click to expand...
 
OP
rst

rst

Youngling
Re: mathematic related questions

Niilesh said:
If the answer would have been two or three digit maybe i could have solved(without hit and trial) it but the answer is in 6 digits!
Click to expand...

i don't like "hit and trial" questions
we should be able to use maths concept in a question

Niilesh said:
If anyone can explain whats written here it would be appreciated(its the solution)
Click to expand...

Yeah

program is better option for such calculation

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NEW OBJECTIVE QUESTION
tetrahedron.PNG

Also plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
 
dashing.sujay

dashing.sujay

Moving
Staff member
Re: mathematic related questions

@Niilesh - The solution is mind boggling. The question is really tough. I tried and left it :|

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NEW OBJECTIVE QUESTION
View attachment 10109

Also plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
Click to expand...

One, and no explanation required I guess.
 
Niilesh

Niilesh

Padawan
Re: mathematic related questions

Another question -
There is a 10-digit number, represented by ABCDEFGHIJ, where each numeral, 0 through 9, is used once. Given the following clues, what is the number?

1) A + D = a square number
2) G + J = a triangle number
3) B + I = an even number
4) E * F = an odd number
5) C * H = a prime number
6) A / G = G / C
7) E + I = B + H

Note: their are more than one answer
 
dashing.sujay

dashing.sujay

Moving
Staff member
Re: mathematic related questions

^If the values aren't in increasing order, then answers can be too many. For instance,
a) 0+1, 0+4, 1+3, 0+9, 1+8, 3+6, 4+5.
Am I getting it right?
 
Niilesh

Niilesh

Padawan
Re: mathematic related questions

^ All the conditions have to be satisfied together :)
 
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Niilesh

Niilesh

Padawan
Re: mathematic related questions

^ Since the question has more than one solution, therefore you will have to apply Hit and Trial.
But conditions removes most of the combinations,
For example C * H = a prime number, so one no. will be 1 and another will be prime.
 
OP
rst

rst

Youngling
Re: mathematic related questions

Niilesh said:
Ans is 1?
Click to expand...
yeah
ans is 1
But I also need explanation

dashing.sujay said:
One, and no explanation required I guess.
Click to expand...

explanation is required

I know ,its more like a practical question
but you can explain
as length of wire and edges of tetrahedron is given

Niilesh said:
Another question -
There is a 10-digit number, represented by ABCDEFGHIJ, where each numeral, 0 through 9, is used once. Given the following clues, what is the number?

1) A + D = a square number
2) G + J = a triangle number
3) B + I = an even number
4) E * F = an odd number
5) C * H = a prime number
6) A / G = G / C
7) E + I = B + H

Note: their are more than one answer
Click to expand...

5) C * H = a prime number
so either C or H= 1

6) A / G = G / C
AC= G^2

if C=1
A=G^2=4,9


possibilities are A=4, G=2, C=1 or A=9, G=3, C=1

take A=4, G=2, C=1

2)G + J = a triangle number
G + J=2+8[as triangular number are 1,3,6,10,15]
clearly J=8

1) A + D = a square number
A + D = 4+0 or 4+5 [as square number are 1,4,9,16]
so D= 0 or 5.........(i)

4) E * F = an odd number
both E and F are odd number-----------(ii)

even number 6 can be only B or I [using i and ii]

3) B + I = an even number
B + I = 6+0 or 0+6-----------------(iii)

using (i) and (iii)
D=5

Also H= 3 or 7 [as H is prime number (if C=1)]-------------------(iv)
7) E + I = B + H

As B, I can be 0 or 6
difference of B and I is 6
so difference of E and H is 6

only left numbers are 3,7 and 9
E ,H can be 3,9
using (iv) H =3
hence E= 9

definitely F=7

Now E + I = B + H
9+I =B+3
6 =B - I

So B= 6
I= 0

Hence ABCDEFGHIJ = 4615972308

As there are more than one answer of the question
we can also try H=1 condition [I get the above answer with condition C=1]
Also can try A=9, G=3, C=1

Niilesh said:
ans is 3
sol. their will be 3 intersection points on each of the 4 lines(so they would be collinear), now every point will have 4 points on old lines(I think you will be able understand what I mean) so only one new line be formed form each point

so ans = 6/2 = 3
Click to expand...

plz explain in simple way
i.e how there are 3 intersection points on each of the 4 lines
every point will have 4 points on old lines
 
Last edited:
Niilesh

Niilesh

Padawan
Re: mathematic related questions

rst said:
As there are more than one answer of the question
we can also try H=1 condition [I get the above answer with condition C=1]
Also can try A=9, G=3, C=1
Click to expand...
H cannot be 1 :)
Second answer is 9817453260

rst said:
plz explain in simple way
i.e how there are 3 intersection points on each of the 4 lines
every point will have 4 points on old lines
Click to expand...
Hopefully this image will solve your problem
*i.imgur.com/AKoD4m1.png
 
OP
rst

rst

Youngling
Re: mathematic related questions

Niilesh said:
Second answer is 9817453260
Click to expand...

Its look like mobile phone number
Its definitely someone mobile number

Niilesh said:
H cannot be 1 :)
Click to expand...

Yeah
may be possible
I didn't try this case

Niilesh said:
Hopefully this image will solve your problem
*i.imgur.com/AKoD4m1.png
Click to expand...

Definitely
Its really helpful

But I think that I even didn't understand the question
According to the question lines are drawn joining the point of intersection of the previous four lines
What is the meaning of this line ??
Can you elaborate it ??
 
Last edited:
Niilesh

Niilesh

Padawan
Re: mathematic related questions

Umm.. I am not sure how can i explain it more properly in words -
new lines are drawn joining the point of intersections of the previous four lines
 
OP
rst

rst

Youngling
Re: mathematic related questions

Niilesh said:
Umm.. I am not sure how can i explain it more properly in words -
new lines are drawn joining the point of intersections of the previous four lines
Click to expand...
no problem
I know its difficult to explain geometrical problem without figure
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OP
rst

rst

Youngling
Re: mathematic related questions

great work
thanks a lot

Now the whole question and its answer is clear to me

rst said:
NEW OBJECTIVE QUESTION
View attachment 10109

Also plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
Click to expand...

ans is 1

Tetrahedron shape is given in the figure
It is 3 dimensional figure
Its a kind of pyramid

total length of wire is 6 m
Each edge of Tetrahedron is 1 m

With the wire first make equilateral triangle of each of side 1m
Then from one vertex of triangle raise the wire 1m to the point O (say)then again join O to other vertex.
now we have to break wire first time
At last with remaining 1m wire join remaing third vertex of triangle to point O
Tetrahedron is formed after cutting wire 1 time

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NEW OBJECTIVE QUESTION
cone+sphere.PNG

Also plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
 
Last edited:
Niilesh

Niilesh

Padawan
Re: mathematic related questions

Its 3.5

join the centre of the sphere to the point of contact then a right angled triangle will be formed
r/(h-r) = Sin(30)
R=H/3= 3.5

___________________________________________________________________________
There is a ten-digit mystery number (no leading 0), represented by ABCDEFGHIJ, where each numeral, 0 through 9, is used once. Given the following clues, what is the number?

1) A + B + C + D + E is a multiple of 6.
2) F + G + H + I + J is a multiple of 5.
3) A + C + E + G + I is a multiple of 9.
4) B + D + F + H + J is a multiple of 2.
5) AB is a multiple of 3.
6) CD is a multiple of 4.
7) EF is a multiple of 7.
8) GH is a multiple of 8.
9) IJ is a multiple of 10.
10) FE, HC, and JA are all prime numbers.
 
OP
rst

rst

Youngling
Re: mathematic related questions

Niilesh said:
Its 3.5

join the centre of the sphere to the point of contact then a right angled triangle will be formed
r/(h-r) = Sin(30)
R=H/3= 3.5
Click to expand...
Absolutely Right
----------------------------------
In detail, answer is:-
*img10.imageshack.us/img10/884/cone21.png
Here AOB is right angled triangle at B
let OB=r
OA=h-r

OB/OA = Sin(30)
r/ (h-r) =(1/2)
2r= h-r
3r=h
r=h/3
r=10.5/3
r= 3.5 cm

Niilesh said:
There is a ten-digit mystery number (no leading 0), represented by ABCDEFGHIJ, where each numeral, 0 through 9, is used once. Given the following clues, what is the number?

1) A + B + C + D + E is a multiple of 6.
2) F + G + H + I + J is a multiple of 5.
3) A + C + E + G + I is a multiple of 9.
4) B + D + F + H + J is a multiple of 2.
5) AB is a multiple of 3.
6) CD is a multiple of 4.
7) EF is a multiple of 7.
8) GH is a multiple of 8.
9) IJ is a multiple of 10.
10) FE, HC, and JA are all prime numbers.
Click to expand...

ans is 5736912480
 
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