What Goes Up . . .
E4 An old friend of mine had a little daughter named Chini when he was just a new friend of mine. Meaning Chini is now married with a couple of kids and lives in Australia. Anyway, to get back to when she was little — she had come over to my house with her parents and, as usual, kept asking me weird puzzling question because she knew I was interested in them. “Would a blind man be able to use invisible ink?” she asked. I thought that a was a nice one but let it go thinking she must have heard it somewhere. Then she goes, “How will he know when the ink’s has finished?” Even better, I thought, before she asked the real punch line: “How can even a non- blind person know when his invisible ink has finished?” Got you too, right?
Meanwhile a hydrogen balloon is rising skywards. Its potential energy is increasing and so is its kinetic energy. Something wrong here somewhere?
DEAR MS ( The problem was: “Given a circle where seven dots are placed anywhere on its circumference, what would be the maximum number of regions into which it could be divided?” — MS)
CIRCULAR-REGIONING- DEPT:
We can find the number of regions by using principal induction. For that, we first have to find the general formula which is ( n4 - 6n3 + 23n2 - 18n + 24)/ 24. So now putting 7 in the formula we get P(7) = ( 2401 - 2058 + 1127 - 126 + 24)/ 24 = 57. Thus, there are 57 regions in a circle when there are 7 points on the circumference of the circle. — Kashish Moolchandani, kashishm68@ gmail. com
( The second problem was: “If 0313 = 1, 7662 = 2, 3213 = 0, 1111 = 0, 6666 = 4, 9881 = 5, 6855 = 3, 7756 = 1, 1012 = 1, 5555 = 0 then what does 2581 = ?” — MS)
LOOPY- NUMBERS- DEPT: While initially baffling, the endgame’s solution turned out to be extremely rudimentary. It is based on the shape of each digit. In order to find the solution, one has to count the number of circles in each number. For instance, the number 8 is made of two circles and the number 6 has one circle which is why 6855 = 3. Therefore, the answer for 2581 will be two as eight has two circles.
— Apoorva Gupta, apoorvag32@ gmail. com
After cracking my head for about an hour I realised the answer has to do with the number of circles in each number and there is no rocket science or high level mathematics involved in it. 2581 = 2 ( number 8 made of 2 circles).
— Priyanka Awatramani, priyankag1010@ gmail. com
( The third one was a rebuff from two readers regarding the level of water falling or rising when an ice cube floating on it melts at 0 degrees C — MS)
SUPERCOOL- ICE- DEPT: As one of the “stupid” readers who attempted to solve the puzzle, treating the liquid at 0 degree Celsius as water and not ice, I would like to point out that liquids can be supercooled and super heated. Meaning, under certain conditions, water can be cooled below zero degree Celsius without freezing and heated above 100 degrees Celsius without boiling. So, unless one wants to nitpick, water can stay in liquid state at 0 degree Celsius.
— Balagopalan Nair K, balagopalannair@gmail.com
Actually the water level neither rises nor falls; it stays the same. The reason an ice cube floats is because its volume has expanded during crystallisation due to the anomalous expansion of the water effect. — Meenakshi Mehta, meenam241@gmail.com ENDGAME( S) 1. A man walked to an automated security gate when a recorded voice uttered “12”. The man replied “6” and was let in. Another man approached the gate and heard “6” to which he replied “3” and was let in, too. Watching this, I went to the gate and heard the voice say “8”. When I replied, “4”, I was not let in. What should I have actually said? — ( Submitted by Sheikh Sintha Mathar,
sheikhsm7@gmail.com) 2. UNCERTAINTY is to HEISENBERG as UNDECIDABILITY is to . . . ?
( Mukul can be reached at mukul. mindsport@gmail. com)