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Topic: solution for IMO and PUTNAM needed
Replies: 11   Last Post: Jul 25, 1996 1:10 AM

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Ted Alper

Posts: 51
Registered: 12/6/04
Re: IMO96 question 1b -correction
Posted: Jul 24, 1996 12:55 PM
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In <gathe.67.1EFF6E35@ul.ie> gathe@ul.ie (Eugene Gath) writes:


>>>b) Prove that the task can be done if r = 73.

>>> 73 = 8^2 + 3^2, so we can change one coordinate by 8 and the other by 3
>>> at each step.


>I write:
>(0,0)->(3,8)->(6,0)->(14,3)->(6,6)->(14,9)->(11,1)->(3,4)->(11,7)->(19,10)
>->(16,2)->(8,5)->(16,8)->(19,0)
>which does it in 13 moves.
>Has anyone got a 12-move solution?
>=============================================================


How about 11?
(0,0) -> (8,3) -> (0,6) -> (8,9) -> (11,1)
-> (19,4) -> (11,7) -> (19,10) -> (16,2)
-> (8,5) -> (16,8) -> (19,0)

You can't do it in fewer, since you will need 8 +3s in the
y coordinate to cancel the 3 -8s in the y coordinate.


Ted Alper
alper@epgy.stanford.edu







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