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> Just Math (2)> Science> Algorithms
A circle with radius 4410001/2 is drawn at on a Cartesian plane with the origin as its centre.

How many lattice points (coordinate with integer coordinates) does it pass?
(No Solution Yet, 1 Comments) Submitted on 2021-09-22 by Danish Ahmed Khan   
Difficulty: 5 of 5 Bonus: Logicians, hats, and numbers (in Logic) Rating: 3.78
Adam, Bob, and Chuck, three perfectly intelligent logicians, are sitting facing each other with a hat on each of their heads so that each can see the others' hats but they cannot see their own. Each hat, they are told, has a (non-zero) positive integer on it, and the number on one hat is the sum of the numbers on the other two hats. The following conversation ensues:

Adam: I do not know the number on my hat.
Bob: I do not know the number on my hat.
Chuck: I do not know the number on my hat.
Adam: I do not know the number on my hat.
Bob: I do not know the number on my hat.
Chuck: I do not know the number on my hat.
Adam: I do not know the number on my hat.
Bob: I do not know the number on my hat.
Chuck: I do not know the number on my hat.
Adam: The number on my hat is 1691.

Adam was correct. What are the numbers on the other two hats?
(No Solution Yet, 20 Comments) Submitted on 2006-08-14 by Avin   
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