Answer One: The Martians’ Apartment
Original Problem
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From statement 4, E lives above B and below A. From statement 1, A does not live above level 3. Thus, B, E, and A occupy the first, second, and third floors respectively. From statements 2 and 4, C lives on the fourth floor and F lives on the fifth floor while D lives on the sixth floor. So the answer is
Albert 3rd floor
Bel 1st floor
Carol 4th floor
Danny 6th floor
Erika 2nd floor
Fido 5th floor
Answer Two: Big and Tiny
Original Problem
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Family A has 10 dwarfs, 4 giants; family B has 4 dwarfs, 6 giants; family C has 1 dwarf and 5 giants.
Full solution will be posted in the future.
Answer Three: Cutting the Cake
Original Problem
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Answer Four: Newcomb’s Paradox
Original Problem
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Answer Five: USA + USSR = ?
Original Problem
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So, what are the hidden digits behind USA, USSR, and PEACE? Let’s see…
We first notice, this is a three digit number plus a four digit number whose sum is a five digit number. Thus, USSA must be over 9000 (and USA over 900), and PEACE must be in the form of 10xx0. As such, we can put P=1, U=9, and E=0.
Secondly, because the unit digit of the sum (E) is 0, we see that A and R must add up to 10. Because 1 and 9 are represented by P and U, A and R must be one of {4,6}, {3,7} or {2,8}. Because in hundreds digit in the sum is also A, we explore the possibilities of A=8, 7, 6, 4, 3, 2 one by one. If A=8, then because U=9, the hundreds digit in USSR (S) must be 9 or 8; but 9 is already represented by U and we gave A the value of 8, we have a contradiction, and so A does not equal to 8. Let’s go to 7. If A=7, then S can only be 8 or 7 (but A=7 so S cannot be 7), but if S=8, then the tens digits in both USA and USSR are S’s, and we then need to carry a one in the addition process and experience furthur conflicts, so A cannot equal to 7. Similarly, A cannot equal to 6 or 4. Then we let A=3, and we can easily see that it does not work either. Finally, we try A=2, then S=3, C=7, and there are no conflicts.
Finally, we can see that this equality becomes 932+9338=10270.
See, not too bad!
Answer Six: Forty+Ten+Ten=?
Original Problem
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29786+850+850=31486
Answer Seven: Urban Planning
Original Problem
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“Ride your brother’s camel!”
Answer Eight: Bad Bird, Bad Bird!
Original Problem
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The car had used up some gas while traversing the first half of the bridge, and is thus less heavy then it was in the beginning. Similarly, we are only able to launch spacecrafts to space because the fuel is consumed during the flight, making the spacecraft less massive as it tries to escape the Earth’s gravitational field.
Answer Nine: Two Unfortunate Men
Original Problem
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It was the cabin of a plane!
Answer Ten: Tricky Summation
Original Problem
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62-64=1 !
