How many three digit

[sanjib]

How many three digit number between 100 and 200 have a digit that is the average of the other two digit.

Need the explanation please that how to deduce it in a succint way.

[maihuna]

How many three digit number between 100 and 200 have a digit that is the average of the other two digit.

Need the explanation please that how to deduce it in a succint way.

For averages to be digits either both end nos are odd or both end nos are even, here we are looking for numbers between 101 and 199 since one end is 1, the other end should be 1/3/5/7/9 so we are looking for 5 such nos. 111 123 135 147 159 so for for middle no.

Similarly for end no since begin is with 1, for end to be an digit the middle no must be one of 1/3/5/7/9 i.e. 111, 132 153 174 195

since 111 is common we have a total of 9 such nos

[majorsheetal]

Is there any easy solution to these type of problems???

[diebeatsthegmat]

How many three digit number between 100 and 200 have a digit that is the average of the other two digit.

Need the explanation please that how to deduce it in a succint way.

a= (B+C)/2
if A=1 so 1+1/2=1 so the number is 111
if A+1 so (2+0)/2=1 so the number is 120 and 102
if A=2 so (1+3)/2=2 so the number is 123and 132
so on we will have 135,153,147,174,159.195
totally we will have 11 number

[majorsheetal]

ok thats really easy ..thanks

[aimscore]

Hi,

If I modify this same question with different nos,

How many three digit number between 200 and 300 have a digit that is the average of the other two digit.

I solve it to get 9 nos.. 222, 234,246,258,210, 243,264,285,201. Please let me know if this is correct.

Are there any other nos that i am missing out..



PS: I am just trying to solve for different nos so that in the future, I should be able to solve a similar problem.

[pesfunk]

Completely correct !!

Hi,

If I modify this same question with different nos,

How many three digit number between 200 and 300 have a digit that is the average of the other two digit.

I solve it to get 9 nos.. 222, 234,246,258,210, 243,264,285,201. Please let me know if this is correct.

Are there any other nos that i am missing out..



PS: I am just trying to solve for different nos so that in the future, I should be able to solve a similar problem.

[Hdim]

Mon Oct 11, 2010 11:29 am

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Hi,

If I modify this same question with different nos,

How many three digit number between 200 and 300 have a digit that is the average of the other two digit.

I solve it to get 9 nos.. 222, 234,246,258,210, 243,264,285,201. Please let me know if this is correct.

Are there any other nos that i am missing out..

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I think you missed 213 and 231