What is the Number? (Problem 1)

Answer 59

• Condition 1 : Is $59$ a prime? $\color{#3D99F6}{\text{Yes}}$
• Condition 2 : Is $5 \times 9 - (5 + 9) \implies$ a prime? $\color{#3D99F6}{\text{Yes}}$
• Condition 2 : Is $5$ a prime and $9$ a prime squared? $\color{#3D99F6}{\text{Yes}}$

The number $29$ is also a candidate, though it is not present in the sequence.

Method 1: Eliminating Condition 1

Since the number is prime and it's the basis of the other two conditions, there are only 8 primes in the sequence : $47, 59, 41, 53, 37, 43, 31$

Then either do:

a): Eliminate Condition 2 - $47, 59, 43, 37, 49$ and $53$ all fulfill this condition then do Condition 3 - $59$ fulfills this condition.

b): Eliminate Condition 3 - $59$ fufills this condition.

Therefore, using Method 1a) or 1b), $59$ is the answer.

Method 2: Eliminating Condition 2

Since Condition 1 is the basis of these conditions, only $47, 59, 43, 37, 49$ and $53$ fulfills this condition.

Then eliminate Condition 3, which leaves us with $59$ .

Therefore, using Method 2, $59$ is the answer.

Method 3: Eliminating Condition 3

Since Condition 1 restrains this condition, $59$ is the number that this condition leaves us with

Therefore, using Method 3, $59$ is the answer.

Therefore, through all methods (whichever you chose), $59$ is the number.