Question

1. what is the mystery number x?

• x has 3 digits.
• the tens digit is half the hundreds digits.
• the number is odd.
• the sum of the digits is 9.

answer: x = ______
jupiter iv page 1

Explanation:

Step1: Define digits

Let the hundreds digit be \( h \), tens digit be \( t \), units digit be \( u \). The number is \( 100h + 10t + u \). Given \( t=\frac{h}{2} \), so \( h \) must be even (2, 4, 6, 8) as \( t \) is a digit (0 - 9). Also, \( h + t + u = 9 \), and \( u \) is odd (since number is odd, units digit is odd: 1, 3, 5, 7, 9).

Step2: Test possible \( h \) values

• If \( h = 2 \), then \( t = 1 \). Then \( u = 9 - 2 - 1 = 6 \) (even, invalid as \( u \) must be odd).
• If \( h = 4 \), then \( t = 2 \). Then \( u = 9 - 4 - 2 = 3 \) (odd, valid).
• If \( h = 6 \), then \( t = 3 \). Then \( u = 9 - 6 - 3 = 0 \) (even, invalid).
• If \( h = 8 \), then \( t = 4 \). Then \( u = 9 - 8 - 4 = -3 \) (invalid, digit can't be negative).

Step3: Form the number

With \( h = 4 \), \( t = 2 \), \( u = 3 \), the number is \( 100\times4 + 10\times2 + 3 = 423 \).

Answer:

\( x = 423 \)