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How many positive integers less than 5,000 have at most two different digits.

 Feb 4, 2019
 #1
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There are

9 1 digit numbers

90 2 digit numbers

252 3 digit numbers

257 4 digit numbers 

 

for a total of 608

 

the 3 digit number breakdown is as follows, n and m are distinct non-zero digits

9 nnn

9*8=72 nnm

9*8=72 nmn

9*8=72 nmm

9 nn0

9 n0n

9 n00

 

I leave working out the 4 digit breakdown to you.

 Feb 5, 2019

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