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Difficulty: MediumOrder and Ranking

A solar energy farm has a continuous linear array of 105105 solar panels. Panel Sigma is currently positioned 43rd43^{\text{rd}} from the left end of the array. Due to a localized upgrade project, the first 1818 panels from the left end and the last 2424 panels from the right end are temporarily removed from the array. In the newly formed, shorter array of remaining panels, what is the position of Panel Sigma from the right end?

Answer: 39

Answer

39
Panel Sigma's original position from the left is 43rd43^{\text{rd}}. When 1818 panels are removed from the front, its new position from the left becomes 43−18=25th43 - 18 = 25^{\text{th}}. The initial total was 105105 panels. After removing 1818 from the left and 2424 from the right, the new total is 105−18−24=63105 - 18 - 24 = 63 panels. Using the standard ranking formula (Total=Left+Right−1Total = Left + Right - 1), the position from the right is calculated as 63−25+1=39th63 - 25 + 1 = 39^{\text{th}}.

Step-by-Step Solution

1
Calculate the new total number of panels in the array.
105−18−24=63105 - 18 - 24 = 63 panels
Removing panels from both ends reduces the overall length of the array.
2
Determine Panel Sigma's new position from the left end.
43−18=25th43 - 18 = 25^{\text{th}} from the left
Removing 18 panels from the left shifts Panel Sigma 18 positions closer to the left end.
3
Calculate Panel Sigma's new position from the right end.
Position from right = 63−25+1=39th63 - 25 + 1 = 39^{\text{th}}
Using the standard ranking formula (Total = Left Position + Right Position - 1), we find the right-side position.

Key Concept

Positional shift and total rank calculation in a truncated linear arrangement

Alternative Method

Instead of calculating the new total, you can determine how many panels are strictly to the right of Panel Sigma. Initially, there are 105−43=62105 - 43 = 62 panels to its right. Removing 2424 panels from the right end leaves 62−24=3862 - 24 = 38 panels to its right. Since there are 3838 panels after it, Panel Sigma must be the 39th39^{\text{th}} panel from the right end.
Estimated Time:1m 0s
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Topics

Order and Ranking

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