[clsuresh]

Folks,

Good morining

Here's comes our next question.

FIND THE SINGLE DIGIT SUM OF THE NUMBER N = 4444^3333

(single digit sum of 3749 = 3+7+4+9= 23 = 2+3 = 5)

Regards,
Suresh

[thakarsagar]

Originally Posted by clsuresh

Folks,

Good morining

Here's comes our next question.

FIND THE SINGLE DIGIT SUM OF THE NUMBER N = 4444^3333

(single digit sum of 3749 = 3+7+4+9= 23 = 2+3 = 5)

Regards,
Suresh

good morning suresh,
looks like i logged on the right time...

Ans is 7....
4444%9 = 7...
3333%4 = 1 (cyclicity of 4 for 7)
=> 7....

regards,
-sagar

[clsuresh]

Hi Sagar,

Good morning Boss.

Sagar, the answer is not 7. Please rethink.

[thakarsagar]

Originally Posted by clsuresh

Hi Sagar,

Good morning Boss.

Sagar, the answer is not 7. Please rethink.

sorry,
it's cyclicity of 3 and not 4...
so 3333%3 = 0...
Answer is 1...

regards,
-sagar

ps: pardon me, am without a pen and a paper ....
fine suresh, am going now...catch you tom...

[clsuresh]

Yes the answer is 1.

Sagar I have a different and simple approach.

Here comes our next basic funda.

All of us know that the remainder obtained when a number is divided by10 is nothing but the unit's digit of that no.

Had u ever thought of the remainder that is obtained when divided by 9. It is nothing but the single digit sum of that number.

For example the single digit sum of 4658 = 4 + 6 + 5 + 8 = 23 = 2 + 3 =5.
Now when 4658 is divided by 9 the remainder is nothing but the remainder obtained when sum of the digits of 4658 i.e 23 is divided by 9 which in turn is nothing but the remainder obtained when 2+3 = 5 is divided by 9.

So that's the funda here folks.

Finally the remainder obtained when 4444^3333 is divided by 9 is nothing but the single digit sum.
4444^3333 % 9
= 7^ 3333 % 9
= 343^ 111 % 9
= 1.
Since the remainder obtained when N is divided by 9 is 1 the single digit sum is 1.

Remember if the remainder obtained is 0 then the single digit sum is not 0 but ofcourse it is 9

[ankit.3k]

finally i have got one question correct.

[clsuresh]

SHE IS SWEET,
SHE IS CUTE,
I LOVE HER,
SHE IS TURNING 59,

HAPPY INDEPENDENCE DAY

[clsuresh]

Guys,

I want a holiday. So nothing from my side for today.

Byeeeeee

[msksent]

The question u have asked is the single digit answer for 4444^3333. It can also be done this way. For 4444 single digit equivalent is 7 and for 3333 it is 3. Hence 7^3 = 343 which is 1. Hence 4444^3333 will have 1 as the answer.

[Mohit102]

Originally Posted by thakarsagar

No suresh, i know the answer for this....but i have not been able to derive it fully...i thought on the following lines...

We need to find it for all the subsets of 1 5 10 and 25 ie 16-1 sets...

using anyone of 1 , 5 10 and 25 -> 4 ways
using 1 and 5 -> 19C1 ways...(its equivalent to solving the equation a + 5b = 100...Now this is limited by the highest coefficient...so divide 100/5 = 20...now any of this 20 i can form a partition...one part been paid by 5 rupee notes and other by 1 rupee notes...)
using 1 and 10 -> 9C1 ways...
using 1 and 25 -> 3C1 ways ...
.
.
.
See, if you can work this ways...
-sagar

NOT QUITE SURE ABOUT BELOW but looks correct to me. . SAGAR could you please confirm the answer.

using anyone of 1 , 5 10 and 25 -> 4 ways
(1,5) = 19 ways ( As 5 has to be used so we can subtract 5 from 100. Rest 95 can be distributed in 95/ 5 = 19 Ways)
(1,10) = 9 Ways ( As above)
(1,25) = 3 Ways (As above)
(1,5, 10) = 17 ways ( 5 + 10 = 15. so 100 - 15 = 85) and 85/5 = 17/
(1,5,25) = 14 Ways
(5, 10) = 18 Ways
(5,25) = 15 Ways
(5, 10,25) = 13 Ways
(10,25) = 5 Ways ( because we have to use 2 25's in this case)

So total = 117 ways

Mohit