For whole numbers a, b you can convert them to a percentage a/b that is then rounded to a whole percent.

Suppose you know a/b = 24%, it may be that b=21 since 5/21 = .238095... but b could not be 22 since 5/22=23% and 6/22=27%.

Still using 24%:
[1] What is the smallest possible value of b?
[2] What is the largest value that b could not be?

Now find the 5 percentages between 0 and 50
[3] that give the largest answers to part [1]?
[4] that give the smallest answers to part [2]?

(In reply to Puzzle Thoughts by K Sengupta)

(3) 49% and 1% with b=66, 33% with b=77 and 20% and 48% with b=78.

Posted by K Sengupta on 2024-07-03 09:07:03