Dapper Diaper Dept.

E4
Happy New Year to you too, people who wished and even those who didn't. This reminds me of a joke about a baby diaper manufacturing company, which announced their new product on a new year's day: a diaper that made a sound whenever it got soiled. They actually called it A Nappy You Hear.
You can stop groaning now because I have something important to say. I was going to talk about how a lot of people growl from time to time, saying they are 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 painted. The cube is taken apart and it is found that 217 of the unit cubes have paint on them. What is the total number of unit cubes?

DEAR MS
(An earlier problem was: "A cube of butter is sliced five times by a butter knife. Into how many pieces at most can that cube of butter be divided if each knife stroke is perfectly straight and the pieces of butter are never rearranged?" In this connection, let me say that 23 people got the wrong answer ranging from 12, 16, 22 and 32 pieces. Only one has got it right so far. - MS)

Cut-Above-The-Rest-Dept:
This can be achieved by using the formula (x^3 + 5*x)/6 + 1, where 'x' is the number of cuts. So the maximum number of pieces that can be obtained in five cuts are 26.
- Saifuddin S F Khomosi, saif_sfk@hotmail.com

(Next: "Which were the only Olympic Games not held in a leap year?" - MS)

Leaping-Games-Dept:
By Olympics, we almost tend to assume it's the Summer Olympics, though, in fact, there are Winter Olympics too. The summer games are always held in leap years except the one held in 1900, which, technically, is not a leap year because 1900 is not a multiple of 200 (or divisible by 400. - MS). Till 1992, both Summer and Winter Olympics were held in the same year but the next winter games, after 1992, was held in 1994. Since then, Winter Olympics is held every four years; not in leap years but between leap years.
- Balagopalan Nair K, balagopalannair@gmail.com

The modern Olympic Games, which started in 1896 and were supposed to be held every four years after that, were next held in 1900. Since 1896 was a leap year, it is assumed that every Olympic Games will take place in a leap year. This is true up to now with one exception - 1900. The reason is while any year divisible by four is a leap year, any year ending in two zeroes has to also be divisible by 400 to be a leap year.
- Harsh Manglekar, harmlekar33@gmail.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. - MS)

Bumper-To-Bumper-Dept:
The front engine keeps the coupling between coaches absolutely taut and the bumpers slack. The back engine keeps the couplings slack and the bumpers taut and touching. Therefore, the  actual distance between the bumpers of the coaches from the front to back will slowly and steadily diminish and till the middle they will be touching. Therefore, half the bumpers from the front to back will not be touching while the remaining half will.
- Dhruv Narayan, dhruv510@gmail.com  

ENDGAME(S)
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 ?

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