Happy New Year to you too people who wished in and even those who didn’t. Which reminds me of this joke about a baby diaper manufacturing company which announced on a new year’s day their new product: a diaper that made a sound whenever it got soiled. They called it A Nappy You Hear.
You can stop groaning now because I have something important to say. Actually I was going to talk about how a lot of people growl in from time to time saying they’re not getting published even though they’d got the right answer but I suddenly realised I’ve run clean out of space, time, energy, inclination, age and money. So next week abs def.
Meanwhile, some unit cubes are glued together to form a larger cube. Some of the faces of the larger cube 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?
THROUGHPUT
(Last fortnight’s problem was: “A cube of butter is sliced five times by a butter knife. Into how many pieces at most can the cube of butter thereby be divided if each knife stroke is perfectly straight and the pieces of butter are never rearranged?” In this connection let me say that 52 people got the wrong answer ranging from 8, 12, 16, 22 and 32 pieces. You know who you are so take your pick. Only one so far has got it correct.)
The precise formula: y = x63/6 + 5x/6 + 1 where x = number of cuts and y = number of pieces. Put x = 5 to obtain y = 26 and that’s the maximum number of pieces possible under the given conditions -- Ajit Athle, ajitathle@gmail.com
(The next problem was: “Which were the only Olympic Games not held in a leap year?”)
In 1900, the summer Olympic games were held in Paris. That is not a leap year as it is not divisible by 400. Regarding winter Olympic games, it started in Chamonix, France in 1924 and continued every four years. All were leap years till 1992. Then in order to alternate summer and winter games in the space of two years, the next winter Olympic was held in 1994 at Lillehammer, Norway. -- Saishankar Swaminathan, saishankar482@gmail.com
. . . In addition, the 1906 Intercalated Olympic games, or 1906 Olympics held in Athens, also come under that category as 1906 was not a leap year. These games were referred to as the Second International Olympic Games” by the International Olympic Committee (IOC). While medals were distributed to participants, they are not officially recognized by the IOC today. -- K Narayana Murty, k_n_murty@yahoo.com
(Among the first five who also got it correct are: Satish Mudaliar, satishmudaliar@yahoo.co.in; P Ganesh Ram, 1969ganram@gmail.com; Shashi Shekher Thakur, shashishekher@yahoo.com; Seshagiri Row Karry, srkarry@yahoo.com; Abhay Prakash, abhayprakash@hotmail.com.)
(The third one was about a train with an engine in front and back with one pulling and one pushing. The question was whether the bumpers of coaches were touching or not.)
Since two engines are needed to haul the train, one can assume that one engine alone cannot support the train on the sloping track. If the front engine can support a certain number of coaches, the coupling between them will be taut as the train pulls them while climbing up the slope and the bumpers of those coaches will not touch each other. The weight of the remaining coaches are supported by the rear engine and therefore, they are pushed by it. Consequently, the bumpers of those coaches will touch one another. Balagopalan Nair K, balagopalannair@gmail.com
The distance between the bumpers of the coaches from the front to back will slowly diminish till at the middle they will be touching. This is because of the pushing effect of the engine at the back. Therefore half the bumpers from the front to back will be not touching while the remaining half will. -- Dhruv Narayan, dhruv510@gmail.com
BUT GOOGLE THIS NOW
1. Easy one. Six consecutive car parking slot numbers are marked 16 06 68 88 ? 98. The question mark means a slot where a car’s already parked so you can’t see the number. What is it?
2. Tough one. What number should replace the question mark at the end of the third row? First row: 5 2 B 5 4 D 5; Second row: 1 8 H 1 3 A 3; Third row: 6 4 G 3 7 F ?
(Sharma is a scriptwriter and former editor of Science Today magazine. mukul.mindsport@gmail.com)