Question

Dorothy has a mysterious $?$ button on her calculator. When she types in an integer and hits the $?$ button, if the input is odd, the calculator outputs $1$ less than triple the input. if the input is even but not divisible by $4$, the calculator outputs $1$ more than half the number. if the input is divisible by $4$, the calculator outputs one-fourth of the input. Dorothy typed in an integer, hit the $?$ button, and saw an output of $13$. What are all possible integers Dorothy may have input?

Answer 1

Given :  mysterious calculator giving different output at Different input

To find : possible inputs  for given output

Solution:

input  odd then  output   less than triple the input

input is even but not divisible 4  then output more than half the input

input is Divisible by 4  then out put one fourth of the input

Integer  typed  = N

Output  = 13

input odd number can be  5 , 7 , 9 and so on

input  even  not divisible by  4 =  22 , 18 , 14 , 10 , 6 , 2

input is divisible by  4 : One possible integer can be   52    

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