If you are an expert in solving Number Place or Sudoku then you must have wondered what can be a general solution to such a problem. The trouble is that the general problem of solving Sudoku puzzles on n2xn2 boards of nxn blocks is known to be NP-complete. In ‘complexity theory’ these are the hardest problems to solve. However, solving Sudoku puzzles can be expressed as a graph colouring problem. The aim of the puzzle in its standard form is to construct a proper 9-colouring of a particular graph, given a partial 9-colouring. The graph in question has 81 vertices, one vertex for each cell of the grid. The vertices can be labelled with the ordered pairs (X, Y), where X and Y are integers between 1 and 9. In this case, two distinct vertices labelled by X,Y and X1, Y1 are joined by an edge if and only if: i) X=X1, or ii) Y=Y1, or iii) [X/3]=[X1/3] and iv) [Y/3]=[Y1/3]. The puzzle is then completed by assigning an integer between 1 and 9 to each vertex in such a way that vertices that are joined by an edge do not have the same integer assigned to them.
PUZZLE 1: Mrs Chewsey has a problem with her little kids when it comes to chewing. Five of the brats choose not to chew cauliflower, and five hate carrots. Of those who chew cabbage only four choose to chew carrots. Of those who chew carrots only three choose cauliflower. And of those who chew cauliflower only two will chew cabbage. Only one of the little Chewseys is not choosy and he happily chews anything. How many little Chewseys are there in the family?
PUZZLE 2: Five friends and their pet dog were spending a night together. They had a packet of biscuits and agreed to open it next morning. One of them woke up at midnight and opened the packet. He divided the content into five equal parts after giving one biscuit to the dog. He ate his share and sealed the packet. Other members of the group repeated the same. What is the least number of biscuits needed?
Solutions on July 18
CORRECT ENTRIES
June 20
Shayak Bhattacharjee; Devika Bharati; Ravi Raja; Vishal Lama; Sreechandra Banerjee; Bodhisattva Chattopadhyay; Abhigyan Mundhra; Abhishek Ray; Dhrubajyoti Daityari; Rajdip and Rajashree Hazra; Marsheley Ray
CORRECT ENTRIES
June 13
Navneet Kumar; Devika Bharati; Janet Chitra Nair; Sreechandra Banerjee; Rajat Tibrewal; Radhika Nangia; Adhikarla Ravi; Sayantan Mondal; Moon Guha; Abhigyan Mundhra; Vishal Lama; Ravi Raja; Anirudh Sharma; Subhash Kumar Chattopadhyay; Suhasini Sen; Surinder Sekhawat; Kumari Meena Sharma; Arundhati Dasgupta; P.T. Lyngdoh
Please mail your entries to knowhow@abpmail.com within 10 days. The address for snail mail entries is Brainstorming, The Telegraph, 6, Prafulla Sarkar Street, Calcutta - 700 001. Don’t forget to mention the date of the puzzle on the top of the envelop. And don’t send one-line answers, we look for complete solutions.
PUZZLE CRACKED
Last week we could not carry the column due to space constraints. This time we have solutions for two consecutive weeks.
Solution for June 13 puzzle: Five Dicky Chicky commercials were shot as follows:
Mon: Jack Alda, George Washingdicky
Tue: Tom Hackman, Johnny Udicky
Wed: Alan Cruise, Clint Eastdicky
Thu: Gene Deniro, Fred Flintdicky
Fri: Robert Nicholson, Elvis Presdicky
Solution for June 20 puzzle: The five honoured musicians, the instruments they play, and their lengths of service with the Summerset Symphony are:
Yolanda Handel; cello; 24 years
Walter Wagner; flute; 18 years
Georgia Ravel; oboe; 12 years
James Schubert; violin, nine years
Maria Bach; clarinet; six years
