New type of numbers

Condition 1: Number is prime $83 \quad 103 \quad 89 \quad \cancel{94} \quad 97$

Condition 2: Odd digit sum $83 \quad \cancel{103} \quad 89 \quad \cancel{94} \quad \cancel{97}$

Condition 3: Only one square digit $\cancel{83} \quad \cancel{103} \quad \boxed{89} \quad \cancel{94} \quad \cancel{97}$

• $89$ is prime as it cannot become an integer by division with any number other than one and itself
• $9$ + $8$ = $17$ , which is odd
• In $89$ , $9$ is the perfect square of $3$ . $8$ is not a perfect square
• Because the number $89$ satisfies all of the conditions, the answer is $89$ .

We are looking for a number that satisfies all the rules listed.

1) It has to be prime

2) It must have a digit sum that is odd

3) The number had exactly 1 perfect square digit

The problem gives us 5 choices, so we start testing.

1: 83. 83 fails the 3rd rule because it does not have a perfect square digit.

2: 103: 103 has an even digit sum, and is greater than 100

3: 89: This passes the test

4: 94: This is not prime, and has 2 perfect square digits

5: 97: This has an even digit sum

So the anwser is 89.

Extra Challenge: Can you find the largest two digit number that satisfies all the conditions? (The answer is mirrored)

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