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)

Comments: ( Back to comment list | You must be logged in to post comments.)

On the assumption all houses were on his side

| Comment 5 of 7 |

Numbers to his houses to his left (1 through 1 less than his) total of numbers to his right (his number +1 through last house):

for n=2:10000

for i=1:n-1

if sum(1:i-1)==sum(i+1:n)

fprintf('%d-%d %d %d-%d\n',1,i-1,i,i+1,n)

end

1-5 6 7-8

1-34 35 36-49

1-203 204 205-288

1-1188 1189 1190-1681

1-6929 6930 6931-9800

Since there were supposed to be between 50 and 500 houses:

The man's house was 204 and the numbers went through #288.

Posted by Charlie on 2022-05-31 12:28:39

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