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Problem of the Week
Problem C
Across the Lane

Lookover Lane divides two rows of houses. Each house on one side of the lane is directly opposite a house on the other side of the lane. The houses are numbered consecutively \(1\), \(2\), \(3\), and so on, along one side. Once the end of that side of the lane is reached, the consecutive numbering continues at the house on the other side of the street opposite the house numbered \(1\). The consecutive numbering then continues along this second side until the last house is numbered.

For example, if there were eight houses on the lane, then House \(1\) would be opposite House \(5\), House \(2\) would be opposite House \(6\), House \(3\) would be opposite House \(7\), and House \(4\) would be opposite the House \(8\).

From left to right, one side of the street has houses
numbered 1, 2, 3, 4 and the other side of the street has houses numbered
5, 6, 7, 8.

However, on the actual lane, House \(37\) is opposite House \(2026\). How many houses are on Lookover Lane?

Theme: Number Sense