How many diagonals does a regular seven-sided polygon contain?
A seven-sided polygon has seven vertices. There are ${7 \choose 2} = 21$ ways to connect the pairs of these 7 points. But 7 of those pairs are pairs of consecutive vertices, so they are counted as sides. So, only $21 - 7 = \boxed{14}$ of these segments are diagonals.
14
Level 3
Counting & Probability
Problem: How many diagonals does a regular seven-sided polygon contain?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine the number of diagonals in a regular seven-sided polygon, we start with the formula for calculating the number of diagonals in an n-sided polygon, which is given by the formula D = n(n - 3)/2. 

In this case, n equals 7, since we are dealing with a seven-sided polygon. 

First, we substitute n into the formula: 
D = 7(7 - 3)/2. 

Next, we simplify the expression inside the parentheses: 
7 - 3 equals 4. 

Now, we multiply 7 by 4: 
7 * 4 equals 28. 

Finally, we divide by 2 to find the number of diagonals: 
28 / 2 equals 14. 

Thus, the total number of diagonals in a regular seven-sided polygon is 14.<|END_OF_LATENT|> The final answer is $14$.