Using colour red blue & green, hw many diff ways can we paint edges of a regular pentagon sch tat no 2 edges meeting at a common vertex are of same colour ?
Without counting rotations and reflections to be same
Let make edges linear _ _ _ _ _
Possible combinations,
For R any R,G,B can appear; First & last and consecutive edges can't be same
R _ R _ _ ways=3*2*1*2*1 R _ _ R _ ways=3*2*1*1*2 R B G B G ways 3*1*1*1*1 R G B G B ways 3*1*1*1*1
____a_b_c___For a=9b= 9, c ranges from 9-0 = 10 valuesfor b= 8, c ranges from 8-0 = 9 values..................for b=0, 1 valueSo, Total 1+2+...+10 = 55 values for a=9Similarly, for a=8, total 1+2+..+9 = 36So, Total = 1+ (1+2) + (1+2+3) +....+ (1+2+...+10) = 220
Underlined one shouldnt be there in total... As it is the case of 000... It wont b a 3 digit no. in that case...
Underlined one shouldnt be there in total... As it is the case of 000... It wont b a 3 digit no. in that case...
Well. that's something that has always intrigued me. I have seen a few questions where 000 is included as a 3 digit number. I know 0 is not a 3 digit number. As @hiteshkhurana82 said OA is 220, so I wonder what could the reason be.
Well. that's something that has always intrigued me. I have seen a few questions where 000 is included as a 3 digit number. I know 0 is not a 3 digit number. As @hiteshkhurana82 said OA is 220, so I wonder what could the reason be.
I guess he said he dnt hav OA...:P Right @hiteshkhurana82 ? Otherwise Explaination is same in my post also bt diff way... N excluding 000...:P
In how many ways can the number 105 be written as a sum of two or more consecutive positive integers?If your answer is No. of odd factors -1 i.e 7 then kindly show that 7 No.'s in detail
4?
105 = 3*5*7
105 = 52 + 53 105 = 34 + 35 + 36 105 = 19 + 20 + 21 + 22 + 23 105 = 12 + 13 + 14 + 15 + 16 + 17 + 18 The other series won't be considered because the question asks for two or more consecutive "positive" integers.
In how many ways can the number 105 be written as a sum of two or more consecutive positive integers?If your answer is No. of odd factors -1 i.e 7 then kindly show that 7 No.'s in detail
In how many ways can the number 105 be written as a sum of two or more consecutive positive integers?If your answer is No. of odd factors -1 i.e 7 then kindly show that 7 No.'s in detail
2k+1 = 105--possible
3k+3 = 105---Possible
4k+7 = 105---NOT
5k+11 = 105---Possible
6k+16 = 105---NOT
7k+22 = 105---Possible
8k+29 = 105---NOT
9k+35 = 105---NOT
10k+9..
I won't write others but I have found 7 such conditions
I misread it as red, blue or green!!
Confused and tedious to edit....