Thirty equally spaced points on the circumference of a circle are labeled in order with the numbers 1 to 30. Which number is diametrically opposite to 7?
At first, I thought about using the circle as a clock to mark the numbers from 1-30, so 12 o'clock is 1/30 and 6 o'clock is 15. As the circle is divided into 30 equal parts, so number 7 should be 7 unit spaces away 1/30 and the opposite number should be 7 units away (clockwise) away from 15 which is 15+7=22. So the opposite number of 7 should be 22!
The extension of the questions
Think about another bigger number, assume the circle represents numbers from 1-100, and find the opposite number of 25, which turns out to be 75. The answer could be solved by both geometrically and algebraically. See the circle draft below. 25 is the 1/4 of 100 so the opposite of 25 on the circle should be 3/4 of 100 which is 75!
What makes a puzzle truly geometric, rather than simply logical?
If there are no numbers representing each space on the circle or there are no particular patterns of the spacing then the puzzle becomes truly a geometric problem.
Thanks!
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