How many numbers are there in all from 6000 to 6999 (both 6000 and 6999 included) having at least one of their digits repeated?

examrobotsa's picture
Q: 36 (IAS/2006)
How many numbers are there in all from 6000 to 6999 (both 6000 and 6999 included) having at least one of their digits repeated?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,4,8,4,2,4,2

keywords: 

{'digits': [0, 0, 3, 2], 'many numbers': [0, 0, 2, 0]}

The question asks for the total numbers between 6000 to 6999, inclusive, that have at least one digit repeated.

Option 1: 216. This number seems to be way too low. This does not seem a correct possible count of four-digit numbers between 6000 and 6999 having some digits repeated.

Option 2: 356. This option also seems quite low. The range from 6000 to 6999 includes 1000 total numbers. It would seem strange for only 356 to have at least one repeated digit.

Option 3: 496. This option seems more reasonable because 504 (1000 minus 496) would be the count of numbers not having any repeated digits.

Option 4: 504. This answer seems to suggest that half of the numbers between 6000 and 6999 include a repeated digit, but it seems more likely that a four-digit number would include at least one repeated digit.

Therefore, it does seem correct that the answer is option 3, 496 numbers.

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