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How many people are living in this village ?
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possofty
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#1
How many people are living in this village ?

(1)The people living in a small village are supporters of either teams A, B, C or D. In terms of political parties, they are supporters of either parties E, F or G. Some of these people are liars while the rest are truth tellers. The liars lie at every answer they give, while the truth tellers always tell the truth.
The questions (first four questions were asked to all of the villagers, next three were asked to all of the male villagers, and the last three were asked to all of the female villagers) and the number of people that answered "yes" are as follows:

Do you support A ? (50 Yes answers)
Do you support B ? (60 Yes answers)
Do you support C ? (70 Yes answers)
Do you support D ? (80 Yes answers)

Do you support E ? (25 Yes answers)
Do you support F ? (30 Yes answers)
Do you support G ? (35 Yes answers)

Do you support E ? (30 Yes answers)
Do you support F ? (40 Yes answers)
Do you support G ? (50 Yes answers)

How many people are living in this village?

PostPosted: Thu Nov 05, 2009 8:37 am  Back to top 
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roah
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#2
answer
160


solution
We do a system of equation.
Notation is natural:
T_{a} - number of truth tellers supporters of A, etc
T_{e}^{m} - number of truth tellers male supporters of E, etc

T_{a} + L_{b} + L_{c} + L_{d} = 50
L_{a} + T_{b} + L_{c} + L_{d} = 60
L_{a} + L_{b} + T_{c} + L_{d} = 70
L_{a} + L_{b} + L_{c} + T_{d} = 80
A sum: T + 3L = 260

T_{e}^{m} + L_{f}^{m} + L_{g}^{m} = 25
... (i'am lazy)
L_{e}^{f} + L_{f}^{f} + T_{g}^{f} = 50
A sum: T + 2L = 210

The rest is clear: T + L = 160


PostPosted: Fri Nov 06, 2009 9:22 am  Back to top 
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possofty
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#3
thank you !

PostPosted: Fri Nov 06, 2009 10:13 am  Back to top 
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