rajatvmittal wrote:NC4=NC12=> Nhas to be 16
now rephrase the question
what is the reminder when 16! is divided by 17 (16+1)
Now 16 ! is a multiple of 16...When a multiple of 16 is divided by 17 than the reminder will be 16. why?
now think what would your answer be if 16 was divided by 17.
same applied here
hence the answer is C => N
Hi rajatvmittal!
Nice intuition solving to find N = 16, but be careful when you think about the remainders. It is not the case that all multiples of 16 will have the remainder of 16 when divided by 17. For example, if I divide 16*17 by 17, the remainder would be 0. In fact, as most remainders work, this remainder will shift by 1 for each increasing multiple of 16 until it hits a multiple of 17 and then it will start over. I'll show you the products and the remainders and I'll let you test it using pen/paper or a calculator!
16/17 --> r16
(16*2)/17 --> r15
(16*3)/17 --> r14
(16*4)/17 --> r13
(16*5)/17 --> r12
(16*6)/17 --> r11
(16*7)/17 --> r10
(16*8)/17 --> r9
(16*9)/17 --> r8
(16*10)/17 --> r7
(16*11)/17 --> r6
(16*12)/17 --> r5
(16*13)/17 --> r4
(16*14)/17 --> r3
(16*15)/17 --> r2
(16*16)/17 --> r1
(16*17)/17 --> r0
I actually don't know of an easier way to solve this problem that to use the MOD function, but that is not something the real test would ever expect, and the calculations are immense!
Basically you could take the numbers in product groups (e.g. {16*15}, {14*13}, {12*11}, (5*4*3*2}, etc), multiply them out and get their remainders when divided by 17. Then, when you have calculated the remainders for all of those groups, multiply the remainders together (in groups if necessary) and find the remainders of those when you divide by 17. And then continue this process until you have a single number.
For this problem I was able to do it in 3 levels of grouping but again, without a calculator, this would take a LONG TIME!
Hope this helps!
Whit
