We Have Lift-Off

Let me extend this problem a little further if it proves to be a little too simple. Let the five elevators be at floor numbers 20, 20, 22, 24 and 21.

E4
Consider a building with 49 floors. It has five elevators on the floors numbered 17, 26, 20, 19 and 31. The elevators open only when ALL of them are on any one of the floors numbered 21, 22, 23, 24 or 25. We have to move TWO elevators such that they both go UP by eight floors or they both go DOWN by 13 floors. If this moving up or moving down constitutes a single move, find a sequence of these moves such that the elevators open.
Let me extend this problem a little further if it proves to be a little too simple. Let the five elevators be at floor numbers 20, 20, 22, 24 and 21. This time the elevator doors open only when all the elevators are at any one of the floors numbered 21, 22 or 23. Our aim remains the same, with the same +8 and -13 constraints applicable to any TWO elevators. Is there a unique solution to the above problems? If yes, prove why.
If no, think of all the stupid classes in school that had to be interrupted in mid-boredom by telling the guy or gal next to you if he or she could draw a certain figure without lifting the pencil off the paper or going over a line twice. Remember? Anyway, it's in fact a problem in flat topology. Having said that, is there a simple rule which can determine if the figure can be drawn or not? For your info, there is.

DEAR MS

(Part of the question was: "They say if you're caught in a thundershower outdoors, you shouldn't stand under a tree. Why? As long as you stay away from the bark, down which a lightning strike might descend, aren't you safe enough?"- MS)
Tree's-A-Crowd Dept:
No, we are not safe enough. Trees attract lightning strikes to themselves. In a downpour, the air is extremely humid. Charges that descend down the bark can get conducted through the water vapour and make their way to your body. You should ideally avoid standing near trees. That reduces the probability of lightning striking you.

• siddhpatkar@gmail.com

(Actually, also because after hitting a tree and reaching the ground down its wet bark, the lightning current spreads out and runs partially horizontally along the ground. Standing anywhere near a tree could then be potentially dangerous. Meanwhile the other question was: "What connection does an elementary form of carbon have with a soccer ball?" - MS)
Carbon-Footprint Dept:
The structure of C-60 Buckminsterfullerene (bucky-ball) molecule has carbon atoms arranged in the shape of a football. This is the connection between an elementary form of carbon with a soccer ball.

• Ayan Joshi, ayanjoshi@yahoo.com

(And finally, we have a deeper insight into that older escalator steps problem. - MS)
Stepped-Up Dept:
The time walking up is t and the time walking down is 2t. Thus, we must set up two equations, one for going up and one for going down. Going down is: x - r (2t) = 50; going up is: x + rt = 125. Cancelling out rt: x = 50; 2x = 250. Thus 3x = 300 and x = 100.

• Ayesha Syed, ?aisha3789@gmail.com

 ENDGAME(S)
Once again two questions on the same theme - chess, this time - and, no, you don't need to be a GM.

1. A rook can move any number of squares horizontally or vertically. If you place a rook on one of the four centre squares of the chessboard, what is the minimum number of moves it needs to pass over all the squares on the board and return to its original square?
2. How many squares and other rectangles are contained on a chessboard? In other words, in how many ways is it possible to indicate a square or rectangle enclosed by lines that separate the 64 unit squares? 

(Get in touch with Mukul at mukul.mindsport@gmail.com 
 

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