/*
Curious numbers in Picat.
"""
Curious Numbers from "Amusements in Mathematics, Dudeney", number 114.
The number 48 has this peculiarity, that if you add 1 to it the result
is a square number, and if you add 1 to its half, you also get a
square number. Now, there is no limit to the numbers that have this
peculiarity, and it is an interesting puzzle to find three more of
them---the smallest possible numbers. What are they?
"""
The least such numbers are:
[
[48,49,7,24,25,5],
[1680,1681,41,840,841,29],
[57120,57121,239,28560,28561,169],
[1940448,1940449,1393,970224,970225,985]
]
Model created by Hakan Kjellerstrand, hakank@gmail.com
See also my Picat page: http://www.hakank.org/picat/
*/
import cp.
main => go.
go =>
Z = findall(X,$curious(X)),
foreach(Num in Z) writeln(Num) end.
curious(LD) =>
LD = [X,A,B,C,D,E],
LD :: 1..2000000,
X + 1 #= A, % if you add 1 to it
A #= B * B, % the result is a square number
X #= 2 * C, % if you to its half
C + 1 #= D, % add 1
D #= E * E, % you also get a square number
solve([constr,split], LD).