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 exactly 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 exactly fill. So go for it Newton!
Throughput
(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 but the solution is too long to run in its entirety.)
For A to think that B can have no way to determine his sum the sum has to be such that any possible two integers more than one adding up to that should not yield a product which could have any unique two factors. Which means that if the sum with A is x then . . . etc . . . etc . . . etc . . . The only such product y yielding a unique answer is 53. That means the two numbers are 4 and 13. -- Dhruv Narayan, dhruv510@gmail.com
(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”)
Lettuce leaves meant for a tossed salad are never frozen. But for cooking and flavouring uses, one may freeze it. The reason why one won’t be able to use the frozen lettuce to make salads is because the freezing process causes ice crystals to form in plant cells. which rupture cell walls. For vegetables like corn or peas, cell wall damage isn’t as visible because these vegetables are high in starch and contain little water. But lettuce has such a high water content that freezing produces just a slimy mess. -- Ajit Athle, ajitathle@gmail.com
On the ‘cerise’ question, I surmised that it would break the all-time record of maximum number of readers with correct answers, but now I think the ‘lettuce’ question will beat that record. Is my conjecture right? -- Abhay Prakash, abhayprakash@hotmail.com (Nope, ‘cerise’ still wins by light decades -- MS)
(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? “)
The lizard takes a spiral path on the log to keep on top. The equivalent path in a 2D plane would along the length of the diagonal of size 200 ft x 10 ft. This would be approximately 200.2498 ft. -- Ravi Nidugondi, ravi.nidugondi@gmail.com
Let us look at the edge of the circular log touching the ground which is tangential to the circle at the beginning and throughout till end. From start to rest, this represents a rectangle 200 ft long and10 ft wide. Presuming the lizard moves at constant speed, it covers the length of the diagonal of this (albeit on the other side of the log). The diagonal is sqrt(200^2 + 10^2) = sqrt 40100 = 200.25 ft. Radius of log has no relevance; it only gives us an idea of how high the critter is from the ground-- Kishore Rao, kishoremrao@hotmail.com
Treating it like the boatman’s problem and using Pythagoras’ Theorem, the distance moved by the lizard is 100 x square root of 4.01, the unit being feet. The answer, correct to two decimal places, is 200.25 feet. -- J Vaseekhar Manuel, orcontactme@gmail.com
But Google This Now
1. An hourglass (hg) floats inside a narrow tube of water. If the tube is inverted the hg no longer floats at first 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?
The writer is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)