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Bob's New House

Bob moved to a new house on another long street and noticed that now
the sum of the house numbers up to his own house, but excluding it,
equals the sum of the numbers from his house to the end of the road,
again excluding his house. If the houses are numbered consecutively,
starting from 1, what is the number of Bob's house?
Find the number of houses on the road, and Bob's house number if
his has 1, 2, 3, or 4 digits.

Source: Similar to a previous problem (3/26/97) from
*The Penguin Book of Curious and Interesting Puzzles*,
David Wells, 1992.

Solution

Mail to Ken