Maths question...

I got 71. I started from 100 and looked down from there so was looking for the highest that would satisfy all the criteria, going by his reply 'not quite'.

I did it by simply writing out the 6 and 8 timetables side by side, and knowing the answer had to be 1 more than a multiple of 5, and 1 less than a common multiple of 6 and 8, I found 71 fairly quickly.
 
71. Answer achieved by a combo of reasoning and minor brute forcing in my head.

Reasoning:

Answer is less than 100 but not much less.

1 book left over with 5 in a box means that the number of books must end in a 1 or a 6.

1 short of a whole number of boxes with 6 in a box rules out numbers ending in a 6 because that would require a number ending in 7 to be a multiple of 6, which can't happen.

The answer therefore ends in a 1.

Brute Forcing:

91 would require 92 to be a multiple of 6. It isn't.

81 would require 82 to be a multiple of 6. It isn't.

71 would require 72 to be a multiple of 6. It is.
71 would require 72 to be a multiple of 8. It is.

Answer found.
 
Angilion said:
71. Answer achieved by a combo of reasoning and minor brute forcing in my head.

Reasoning:

Answer is less than 100 but not much less.

1 book left over with 5 in a box means that the number of books must end in a 1 or a 6.

1 short of a whole number of boxes with 6 in a box rules out numbers ending in a 6 because that would require a number ending in 7 to be a multiple of 6, which can't happen.

The answer therefore ends in a 1.

Brute Forcing:

91 would require 92 to be a multiple of 6. It isn't.

81 would require 82 to be a multiple of 6. It isn't.

71 would require 72 to be a multiple of 6. It is.
71 would require 72 to be a multiple of 8. It is.

Answer found.
Click to expand...

You Smort :p
This is how I did it basically.
 
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