Problem: A marshmallow has the shape of a cylinder with a diameter of 5 and height of 3. A dessert is made with 24 marshmallows consisting of two stacked 3 x 4 arrays placed on a tray. Chocolate is then poured from on top to fill the gaps between the stacked marshmallows. The question is, what is the volume of chocolate?
To get an idea of what the top view would look like, draw four rows of three circles each representing the tops of the top layer of 12 marshmallows. You know the diameter and height of each marshmallow, and you know they're two layers deep, and now you can see the six gaps between them that the chocolate has to fill. So, go for it Newton!
(The problem was to find the two numbers between 0 and 20 whose sum was known to A and the product to B with the following subsequent conversation: A: "I see no way you can determine my sum." B: (one hour later) "I know your sum." A: (some time later) "Now, I know your product." So far, only one person has got it right. - MS)
The conversation between A and B has the catch and clue tending to the solution. From A's statement ("I see no way you can determine my sum"), we can deduce that the product is not the product of two primes. B's statement ("I know your sum") implies that the sum must be an odd number, because every even number can be written as the sum of two primes (according to Goldbach's Conjecture). Then A says: "Now, I know your product", indicating that the information is adequate for A and B to find the two numbers. The numbers are 4 and 13.
- Priyanka Awatramani, firstname.lastname@example.org
(The other problem was: "What's the only vegetable or fruit that's never sold frozen, canned, bottled, processed, smoked, sundried, salted, stuffed, pickled, cooked or in any other form but fresh? And let's not have stuff like goji berries, sea kelp, chia seeds, etc." - MS)
Lettuce is the only vegetable in this world that is never sold frozen, canned, smoked, sundried or in any other form but fresh.
- Akshit, email@example.com
I think it's lettuce. I am not sure if it is or why but I remember reading this somewhere. I hope this gets planted in the paper. Excuse the pun.
- Bawse Gautham, firstname.lastname@example.org (Well, since you put the seed of the idea in my head, consider it done. - MS)
The vegetable is lettuce. The high water content of lettuce (94.9 per cent) creates problems when attempting to preserve the plant - it cannot be successfully frozen, canned or dried, and must be eaten fresh.
- Jaelyne Tauro, email@example.com
(The last one was: "While a log two feet in circumference and 10 feet long rolls two hundred feet down a mountainside, a lizard on top of the log goes from one end to the other, always remaining on top. How far does the lizard move?" - MS)
Think of the cylindrical log as a rectangle, when rolled out covering a distance of 200 feet. The surface area forms a rectangle with length 200 feet and breadth 10 feet. The lizard has to travel in a spiral to reach the other end as well as to stay on top. This course is a diagonal of (200*10) feet. So, the distance the lizard moves is the hypotenuse of a right triangle whose sides are 200 feet and 10 feet. The answer is 200.25 feet.
- Saifuddin S F Khomosi, firstname.lastname@example.org
The lizard travels a distance equivalent to the hypotenuse of a right-angled triangle, with the other two sides as 200 feet and 10 feet. Hence, the distance travelled is approximately 200.25 feet.
- Minu Moosa, email@example.com
1. An hourglass (hg) floats inside a narrow tube of water. If the tube is inverted, the hg no longer floats till all the sand has poured into the lower section - even though its buoyancy remains the same because the volume has not changed. Why does this happen?
2. Why do the ripples on the sand at the bottom of streams travel upstream?
(Mukul can be reached at firstname.lastname@example.org)