Imagine a metal cube that has a 3x3 grid drawn on each face. There are thus 9 equal squares on each face of the cube, 54 squares in all. If you lay the cube on a flat surface and place a magnetic chess knight on the centre square of the top face of the cube, what is the maximum number of moves that the chess knight could complete if it makes only legal chess moves, lands on no square more than once, and makes its last move so that it lands on the square that it began on?
The knight may move from face to face of the cube as if each face were a continuous flat surface. Each time that the knight makes a move that puts it on a new face that cube face is turned so that it becomes the top face. Only consider the knight to have landed on a square when it is placed on that square as a result of completing that turn’s move, of which there is 1, not 3. Example: The 1st square the knight lands on cannot be on the face on which it began.
Throughput
(The good news is the hiker problem has finally been stung out of you with my carefully poisoned darts aimed at your prefrontal cortex. Oh well, at least something worked.)
It takes 54 days to set up hoards and cross the desert. He stores 33 days’ supply of food and water at the first base, at a distance of 1 day’s travel from base camp, taking 21 days, 10 up and down trips and 1 one way trip. For this he has to begin with 54 days’ supply, because on each trip he carries 5 days’ supply, deposits 3 days’ supply at the camp and uses up 2 days’ supply for the up and down trips and on the one way trip he carries 4 days’ supply and deposits 3 days’ supply at the camp using only 1 days supply on travel. At the second base . . . (Yeah yeah we get it you got it. -- MS) . . . Thus, he takes 54 days (21 days to the first base, 13 to the second, 7 to the third, 5 to the fourth, 3 to the fifth and etc etc etc) to complete his journey. -- Balagopalan Nair K, balagopalannair@gmail.com
(The second problem was: “Consider the following five words: BASIC, ELF, HAITI, KILL, NO, TOFU. Now which of the following six words properly completes the above sequence: QUARTER, QUICK, QUARREL, QUAINT, QUIBBLE, QUERY?”)
QUARTER completes the given sequence as the sixth word -- ie, in between the words NO and TOFU. Each word in the sequence begins with one letter of the alphabet and ends with the letter that would come next in the alphabet. Also the first letters in each word of the given sequence are separated by two successive letters of the alphabet -- ie, the letters B, E, H, K, N, Q and T have two letters of alphabet in between them. -- Narayana Murty Karri, k_n_murty@yahoo.com
I never thought this question could be this naive, going by your norms. -- Seshagiri Row Karry, srkarry@yahoo.com (That’s because my “norms” often means that I end up getting screamingly silent responses till I finally goad you into further inaction! -- MS)
(Among the first 10 who also got it correct are: Raghunath K, rakhunath.k@gmail.com; Hemalatha T, hemalatha1956@gmail.com; Murali S L, murali_sl@yahoo.co.in; Sudha Gopakumar, sudhagkumar@gmail.com; Altaf Ahmed, ctrlaltaf@yahoo.in; Sanath Kumar, sanathkumarts1958@gmail.com; Dhruv Narayan, dhruv510@gmail.com; R Viswanathan, guruviswa@gmail.com; Neethi Balagopal, neethibala@gmail.com; Dr P Gnanaseharan, gnanam.chithrabanu@gmail.com.)
(The third one was: “If a juggler juggles three different coloured objects, how many throws are necessary to return the objects to their starting positions if . . .” etc)
The answer to the juggler problem is 6. Each of the three balls needs one throw to go to the hand other than the hand from which it was thrown and one throw each to be thrown back to the original hand. Three balls and two throws each make it six throws. -- Abhay Prakash, (abhayprakash@hotmail.com
But Google This Now
1. ?, LI, MA, NA, AM, NA, HG, YD, DE, IR, NI, NA, DA (Hint: Tianzhu honcho)
2. A cup of wine is suspended over another cup of equal capacity full of water. Through a very small hole in the bottom, wine drips into the water, and the mixture again drips out of a tiny hole in the lower cup at the same rate. When the wine cup is completely empty, what part of the content of the lower cup is water? (Assume wine and water mix instantly.)
(Sharma is a scriptwriter and former editor of Science Today magazine mukul.mindsport@gmail.com)