perplexus.info :: Just Math : Last house on the street

Last house on the street (Posted on 2022-05-31)

The great Dudeney, bless his soul, created, inter alia, the following puzzle:

There was a man who lived on a XXXX street numbered 1,2,3 … etc. on his side and all the following numbers on the other side of him. The numbers on both sides added to exactly the same amount. What was the number of the last house?

I have slightly changed the original wording and also took the liberty of coding a single 4 letter word of his text to avoid getting a trivial solution.
I ask for a solution which is over 45. The upper limit stays open. So:

a. Provide an answer (or answers) 46 and up.
b. What word was replaced by XXXX?

Bonne chance!

No Solution Yet Submitted by Ady TZIDON

Rating: 4.0000 (1 votes)

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Possible Solution

| Comment 1 of 7

Equivalently, n(n+1)=(n+k)(n+k+1)/2, a Pellian with solutions{k,n}=

{1,2}{6,14}{35,84}...

Solutions for the last house number are (n+k), so the smallest larger than 45 is 119: sum(1 to 84) = 3570 = sum(85 to 119), a LONG street.

Edited on May 31, 2022, 8:43 am

Posted by broll on 2022-05-31 08:42:43

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