536 Puzzles and Curious Problems

266 Answers

170. ANOTHER STREET PUZZLE

On the odd side of the street the house must have been No. 239, and there
were 169 houses on that side. On the even side of the street the house must
have been No. 408, and there were 288 houses.
In the first case, find integral solution of 2x^2 - 1 = y2. Then we get the
answers:

x = Number of houses. y = Number of particular house.

1......................... 1

5......................... 7

29 ......................... 41

169 ......................... 239

985 ......................... 1,393

and so on.
In the second case, find integral solution of 2(X2 + x) = y2.
Then we get the answers:

x = Number of houses. y = Number of particular house.

1........................ 2

8 ........................ 12

49........................ 70

288 ........................ 408

1,681. ....................... 2,378

and so on.
These two cases, and the two previous puzzles, all involve the well-known
Pellian equation and are related.

171. CORRECTING AN ERROR

Hilda's blunder amounted to multiplying by 49, instead of by 409. Divide

the error by the difference (328,320 by 360) and you will get the required

number-912.

172. THE SEVENTEEN HORSES

The farmer's seventeen horses were to be divided in the proportions 1.-2, \-3, ~.