Grades 9-10 Video Solutions 2014-Levels 9&10 Video Solutions 2014 problem16

Levels 9&10 Video Solutions 2014 problem16

Video Transcription

Video Summary

The problem involves determining which number is opposite 14 on a special die, where numbers on opposite faces sum to the same prime. Equations are set up for 14, 35, and 18 with primes on opposite faces. Testing possible prime values, only \( X = 23 \) satisfies the condition: \( 14 + 23 = 37 \) and \( 35 + 2 = 37 \). By determining \( Z \), opposite 18, is \( 19 \) also sums correctly to 37. All numbers (23, 2, 19) are prime, solving for the opposite of 14. The answer is 23.

Keywords

special die

opposite faces

prime sum

number 14

opposite 23