No no no no no, not so fast. You think by pretending that among the three problems given one didn’t exist, isn’t going to cut any global warming from the Arctic. We all know what you did instead: you said, let’s just hit the two easy fricking ones and hope to hell some other freaky nerd’s going to fill in the blanks on the third and do the nerdful. SoRRRy -- not going to happen. In other words, here it comes again, the alternative facts division -- aka your worst nightmare. Think again.
A hiker wants to walk across a desert, a journey of 10 days. He can only carry five days worth of food and water, so he will have to hike part way across and leave food caches to pick up later. How long will it take him to set out the caches and cross the desert? (However, to increase your bad karma the answer may be 54. But why?)
THROUGHPUT
(The cold leftover was: “Some unit cubes are glued together to form a larger cube. Some of the faces of this are then painted. The cube is taken apart and is found that 217 of the unit cubes have paint on them. What’s the total number of unit cubes?”)
The total number of unit cubes is 729 -- forming a bigger cube of 9 x 9 x 9. Three contiguous faces of the larger cube are painted, Thus a total of 243 faces of the unit cubes will be found to be painted. Out of these 1 unit cube will have three faces painted, 24 unit cubes will have two faces painted and 192 unit cubes will have paint on only one face. Hence, the total number of unit cubes that will have paint on them will be 1 + 24 + 192 = 217. -- Dr P Gnanaseharan, gnanam.chithrabanu@gmail.com
There are 729 unit cubes. Three adjacent surfaces are coloured. In a cube made of n*n*n unit cube with surfaces numbered like a die, the surfaces 1 to 6 have n^2, n(n - 1), (n - 1)(n - 1), (n - 1)(n - 1), (n - 1)(n - 2) and (n - 2)(n - 2) unit cubes. By taking n^3-(n - 2)^3 > 217, we get total surface as 218 for n = 7 which is ruled out. So, n is more than 7. By taking n = 8, no combination of surfaces gives 217. By taking n = 9, the surfaces are 81, 72, 64, 64, 56 and 49. The sum of the first three adjacent surfaces is 217 unit cubes. Total number of cubes = 9*9*9 = 729. -- Abhay Prakash, abhayprakash@hotmail.com
(The simple second one was: “SUM = 5187, CUBE = 630, MANY = ?”)
Answer: MANY = 4550. Reason: M = 13th alphabet, A = 1st alphabet, N = 14th and Y = 25th. So the answer is the product of 13, 1, 14 and 25 = 4550. -- Rekha G, g.rekhapai@gmail.com
MANY should be 4550. Because the product of the numbers are represented by the substitution of alphabets by their corresponding numbers. It’s too easy. At least you could have substituted the numbers backwards! -- Dhruv Narayan, dhruv510@gmail.com
(Among the FF who also got it C are: Hemalatha T, hemalatha1956@gmail.com; Shubhashish Mohanta, shubhashishmohanta@rediffmail.com; Shashi Shekher Thakur, shashishekher@yahoo.com; Kishore Rao, kishoremrao@hotmail.com; Seshagiri Karry, srkarry@yahoo.com.)
(And the third problem was: “In flush, a trio is considered higher than a colour sequence. Logically, a hand with a lower probability should be considered higher in value, right? But some flush players say that people get trios more often. Are they right?”)
There are 52 cards in a deck. The total number of three-card hands from a deck of 52 cards = 52C3 = (52*51*50)/6 = 22100. The number of trios such as three aces that can be obtained out of four aces in a deck = 4. The total number of trios in a deck = 13*4 = 52. Thus the probability of a trio = 52/(22100) = 0.24%. The number of colour sequences of three adjacent cards in a suit = 12. The total number of colour sequences in a deck = 12*4 = 48. Thus the probability of a colour sequence = 48/(22100) = 0.22% < 0.24%, the probability of a trio. Hence the flush players are right in that they get trios more often than colour sequences. -- K Narayana Murty, k_n_murty@yahoo.com
BUT GOOGLE THIS NOW
1. 4, 5, 35, 56, 83, ? (Hint: Mensa) (And yes, very tough.)
2. Find a famous Greek mythical act of heroism in the following nonsensical sentence: “Provide men the use so toleration finds residence free of misleading theories gift of decried species.”
(Sharma is a scriptwriter and former editor of Science Today magazine. mukul.mindsport@gmail.com)