Mindsport

E4

In the glorious tradition of this column's constant teetering on the tripwire of correctly loopholed illegality, may I present a way out for laggards. Suppose you have some immediate work, report or article to submit but aren't fully done yet. Don't panic. Simply send the incomplete stuff to this site which then carefully corrupts it so that when the end-reader opens it, he or she can't seem to access it. They think you delivered on time but that they had a technical glitch. Meaning, you get some extra time to send it again. Cool, no? (Want more info? Bet you do!)

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Now, to less important things as usual. A vessel contains a mixture of vinegar and water. Had there been a litre more of vinegar and a litre less of water, the ratio of vinegar to water would have been 7:8. But had there been a litre more of water and a litre less of vinegar, the ratio would have been 2:3. What was the original mixture in litres?

DEAR MS

(The older gen problem was: "A cylindrical marshmallow has a diameter of 5 and height of 3. A dessert is made with 24 marshmallows consisting of two stacked 3x4 arrays. Chocolate is poured filling the gaps between stacks. What is the volume of chocolate?" - MS)

Chox-Stax-Dept:

I would start by imagining a cuboid around the entire dessert, touching the outer surface of the entire marshmallow stack. Its dimensions would be 20H x 15W x 6H (diameter of four marshmallows x diameter of three marshmallows x height of two stacks). A pictorial representation of the same would demonstrate that the total gap between the marshmallows is equal to the total gap outside the marshmallow stack touching the surface of the imaginary cuboid. On calculating the difference between the volume of the cuboid and the volume of 24 marshmallows and then halving the value, we get the

volume of the chocolate as approximately 193.14 units.

- Minu Moosa, minu.moosa@gmail.com (Yes, Apurva J, tsunamiapurva@gmail.com, you also got it almost correct. - MS)

(The other puzzle was: "How can you show that, in any year, the same days of the month in March and November fall on the same day of the week?" - MS)

Day-By-Day-Dept:

With seven days in a week, all months except for non-leap-year February have a few days more than a number of exactly complete weeks. So the months with 30 days (April, June and September) have two days more than exactly four weeks. The months with 31 days (March, May, July, August and October) have three days more than exactly four weeks. All of the 'extra' days (3*2; 5*3) add up to 21 extra days, or exactly three weeks. So, whatever day of the week was March 1 will be the same day on which November 1 occurs. And so forth.

- Jaelyne Tauro, jaelynetauro@gmail.com

(Among the first five who also got it correct are: Alifya Taher, talifya@gmail.com; Siddharth Patkar, siddhpatkar@gmail.com; Fathma Palot, fathmapalot@gmail.com; Sheikh Sintha Mathar, sheikhsm7@gmail.com; Ramesh S Mahalingam, ramesh@idealmc.com. - MS)

(The third problem was: "A slice of uniform thickness of 1 cm is cut from a sphere of diameter 10 cm. What is the curved area of the slice?" - MS)

Slice-Of-Dept:

Since the diameter of the sphere is 10 cm, its radius R is 5 cm and the curved surface area of the slice is 2pi*5 = 10pi = 31.42 square cm. As the curved area is 2piR*1 (1 being the thickness), we can see that it depends only on the radius of the sphere and the thickness of the slice and is independent of how far from the centre of the sphere the slice is cut.

- Balagopalan Nair K, balagopalannair@gmail.com

ENDGAME(S)

1. What do the following words have in common: Bedecked, Icebox, Choice, Kidded?

2. A circular fort of diameter 6 kms has two gates only: one in the north and the other in the south. A big tree stands 2 kms north of the north gate. What distance must be covered by a soldier walking east from the south gate to see the tree without obstruction?

(Mukul can be reached at mukul.mindsport@gmail.com)