Number divisible by 2-13 puzzle

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Number divisible by 2-13 puzzle

Teacher writes a number on board and ask 12 students, one by one, "is it present in table 2?" to first student, "is it present in table 3?" to second student, and so on till the twelveth student for table 13.

All student says "yes".

Finally, the teacher remarks that all except consecutive two of the students were right. What was the least number that the teacher wrote on the board? And which two tables that do not contain the number?
rjamil

Posts: 383
Joined: 15 October 2014
Location: Karachi, Pakistan

Re: Number divisible by 2-13 puzzle

If it's not divisible by 2 or 3, then it's also not divisible by 6. If it's not divisible by 3 or 4, then it's also not divisible by 12. If it's not divisible by 4, it's not divisible by 8 or 12. If it's not divisible by 6, then it is either not divisible by 2 or 3 or both. Therefore, the two numbers are 7 and 8, and the lowest number is (2^2)*(3^2)*5*11*13=25740.
3dsudoku

Posts: 4
Joined: 11 March 2019

Hi 3dsudoku,