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Charlie presents his solution here. My solution is below:
Lets call the coins A, B, C, D, E, F, G. First weigh A+B vs C+D.
Case 1: A+B=C+D Make the second weighing A+C vs E+F.
Subcase 1-1: A+C=E+F: B and D are the two light coins.
Subcase 1-2: A+C>E+F: Make the second weighing E vs F. If E=F then they are the two light coins. If E>F then F and G are the two light coins. If F>E then E and G are the two light coins.
Subcase 1-3: E+F>A+C: Make the second weighing A vs C. If A=C then they are the two light coins. If A>C then B and C are the two light coins. If C>A then A and D are the two light coins.
Case 2: C+D>A+B Make the second weighing A+E vs F+G.
Subcase 2-1: A+E=F+G: A is one of the light coins. Weigh F vs G to find the other.
Subcase 2-2: A+E>F+G: B is one of the light coins. Weigh F vs G to find the other.
Subcase 2-3: F+G>A+B: Make the third weighing A vs B. If A=B then they are the two light coins. If A>B then B and E are the two light coins. If B>A then A and E are the two light coins.
Case 3: A+B>C+D Make the second weighing C+E vs F+G.
Subcase 3-1: C+E=F+G: C is one of the light coins. Weigh F vs G to find the other.
Subcase 3-2: C+E>F+G: D is one of the light coins. Weigh F vs G to find the other.
Subcase 3-3: F+G>C+D: Make the third weighing C vs D. If C=D then they are the two light coins. If C>D then D and E are the two light coins. If D>C then C and E are the two light coins. |
