Answer / guest

Prove it using the mathematical induction.

First here are a couple of things to note:

[1] A number whose digits add up to a multiple of three is
divisable by 3.

e.g. 369: 3+6+9=18: 1+8=9 which is a multiple of 3 hence 369
is divisable by 3.

[2] Whenever a number (X) is multiplied with another number
(Y) then the product (X*Y) will have all the factors of X as
well as all the factors of Y in its set of factors.

e.g. if X has factors of (1,P,Q,X) and Y has factors of
(1,Q,R,Y) then X*Y has factors of (1,P,Q,Q,R,X,Y).

Let

N = any series of digits (e.g. N=369)

D = the number of digits in N (e.g. if N=369 then D=3)

P = is a number constructed in the following way : a 1,
followed by (D-1) 0s, followed by another 1, followed by
(D-1) 0s, followed by another 1. (e.g. if N=369 then D=3 and
P would be 1001001) Note that P will always be divisible by 3.

Also, if we multiply N with P we are essentially repeating N
for (D-1) times.

e.g. if N=369 then D=3, P=1001001 and N*P=369369369

Let's start with N=111. It is clear that N is divisible by
3. (From [1])

Also, D=3 and P=1001001

N*P=111111111 (9 times)

The resulting number 111111111 must be divisible by 9 as N
and P both are divisible by 3.

Now, let's start with N=111111111. It is clear that N is
divisible by 9.

Also, D=9 and P=1000000001000000001

N*P=111111111... (27 times)

The resulting number 1111111... (27 times) must be divisible
by 27 as N is divisible by 9 and P is divisible by 3.

Repeat the same procedure for N=1111111... (27 times) The
resulting number 1111111... (81 times) must be divisible by
81 as N is divisible by 27 and P is divisible by 3.

Similarly, for N=1111111... (81 times) The resulting number
1111111... (243 times) must be divisible by 243 as N is
divisible by 81 and P is divisible by 3.

Thus, 1111111... (243 times) is divisible by 243.

Answer / madman042262

1111....n times(n=243) divided by 243
>>
2+4+3=9
2+4+3=9
.............. 1n/243 where addition of 243 is 9
.............. 1(9)/9=1?
___________________________________________is this correct?

Answer / karthik

factors of 243 is 3^5(3*3*3*3*3) (i.e) 3 is the divident of 243.
.
. . the number (111111.....(243 ones)) is also
divisable by 243.

why i am saying is the total addition of a given
number is divisible by 3.so, definately i say that the given
number is divisal by 243(it is also divisable by 3).

One of the four people - Mr. Clinton, his wife Monika, their son Mandy and their daughter Cindy - is a singer and another is a dancer. Mr. Clinton is older than his wife and Mady is older than his sister. 1. If the singer and the dancer are the same sex, then the dancer is older than the singer. 2. If neither the singer nor the dancer is the parent of the other, then the singer is older than the dancer. 3. If the singer is a man, then the singer and the dancer are the same age. 4. If the singer and the dancer are of opposite sex then the man is older than the woman. 5. If the dancer is a woman, then the dancer is older than the singer. Whose occupation do you know? And what is his/her occupation?

2 Answers  

---

Find the smallest number such that if its rightmost digit is placed at its left end, the new number so formed is precisely 50% larger than the original number.

9 Answers   CTS, Google,

---

A cube is made of a white material, but the exterior is painted black. If the cube is cut into 125 smaller cubes of exactly the same size, how many of the cubes will have atleast 2 of their sides painted black?

3 Answers   Infosys,

---

Mr. Kamal Kishore rents a private car for Andheri-Colaba- Andheri trip. It costs him Rs. 300 everyday. One day the car driver informed Mr. Kamal Kishore that there were two students from Bandra who wished to go from Bandra to Colaba and back to Bandra. Bandra is halfway between Andheri and Colaba. Mr. Kamal Kishore asked the driver to let the students travel with him. On the first day when they came, Mr. Kamal Kishore said, "If you tell me the mathematically correct price you should pay individually for your portion of the trip, I will let you travel for free." How much should the individual student pay for their journey?

2 Answers   Freshdesk,

---

agar aapne kabhi kisi se saccha pyar kiya hai to is gaane ko complete karo K---N -O --H--T - --G--T---I-A J---N T--S-- S----H--

2 Answers  

---

---

Love love it.. friends need it.. relationing start with it.. life ends with it..

15 Answers  

---

We have 2 poles 5 m and 7 m height ropes are connected from top of one to tthe bottem of another find the intersection height of those poles.

5 Answers   Patni,

---

agar aapse wo insaan i love you kahe jis se aap pyar nahi karte to aap uska bina dil dukhaye kya jawab doge?

11 Answers  

---

5. There are e 3 jars of diferent sizes. one jar holds 8 liters of milk, the other 2 jars of 5 liters and 3 liters are empty. there is no measuring level or marks in all the jars. Jugle between these 3 jars and get 2 jars containing 4 liters each at the end.

7 Answers   Nutanix,

---

A polygon has 1325 diagonals. How many vertices does it have?

1 Answers   Samsung,

---

Scientist decided to do a study on the population growth of rabbits. Inside a controlled environment, 1000 rabbits were placed. Six months later, there were 1000Z rabbits. At the beginning of the 3rd year, there were roughly 2828Z rabbits, which was 4 times what the scientists placed in there at the beginning of the 1st year. If Z is a positive variable, how many rabbits would be there at the beginning of the 11th year?

1 Answers  

---

why the students are lag for answering this type of questions?

5 Answers   Honeywell,

---