Number guessing is a popular game between elementary-school kids. Teachers encourage pupils
to play the game as it enhances their arithmetic skills, logical thinking, and following-up simple
procedures. We think that, most probably, you too will master in few minutes. Here’s one
example of how you too can play this game: Ask a friend to think of a number, let’s call it n0.
Then:

1. Ask your friend to compute n1 = 3 ∗ n0 and to tell you if n1 is even or odd.

2. If n1 is even, ask your friend to compute n2 = n1/2. If, otherwise, n1 was odd then let your
friend compute n2 = (n1 + 1)/2.

3. Now ask your friend to calculate n3 = 3 ∗ n2.

4. Ask your friend to tell tell you the result of n4 = n3/9. (n4 is the quotient of the division
operation. In computer lingo, ’/’ is the integer-division operator.)

5. Now you can simply reveal the original number by calculating n0 = 2 ∗ n4 if n1 was even, or
n0 = 2 ∗ n4 + 1 otherwise.

Here’s an example that you can follow: If n0 = 37, then n1 = 111 which is odd. Now we can
calculate n2 = 56, n3 = 168, and n4 = 18, which is what your friend will tell you. Doing the
calculation 2 × n4 + 1 = 37 reveals n0.