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Problematics | A to Z of word hunting
This week, a somewhat challenging juggle for word puzzlers, and some easy mathematics concerning a quarrel on a date gone wrong
Word puzzles tend to be usually easier than numerical ones, but there are exceptions. This week’s game may be one of them. It is a pangrammatic crossword, which means there are 26 blank cells and these are to be filled up with 26 different letters, or each letter once.
We had an earlier such pangram in Problematics some three years ago, after which a couple of readers wrote back that it took them seconds to solve what I took hours to create. The one I have created for this week took me much longer than the last one. It will be hopefully more challenging to readers, but it should be gettable.
#Puzzle 170.1
We have already discussed the rules: all 26 letters from A to Z, each letter exactly once. Although a couple of entries might look tricky, they are all English words found in the Chambers Dictionary. No clues about their meanings are given, since the puzzle is about juggling a known set of letters. Just one hint for now: the longest word is a medical adjective.
In the illustration, the red cells are for the high-value letters in Scrabble, which as players know are J (value 8), Q (10), X (8) and Z (10). I have also highlighted in yellow the cells where the vowels must go. I made an exception for Y (which many consider the sixth vowel) and entered the letter in the crossword to give you a start.
Please fill up the other 25 cells and send me the completed grid. Remember: recognised dictionary words only.
#Puzzle 170.2
A young man picks up his date from her home, planning to watch a movie together. In order to spend more time together, they decide to walk to the cinema rather than catch a bus or the Metro. They do a brisk 9 km/hour and reach the cinema on time. It is at the ticket counter that the trouble starts.
He asks her for the price of her ticket. She refuses, reminding him that it was his idea to take her out. They quarrel for 15 minutes at the cinema before they start walking back to the young woman’s home. Quarreling away, stopping every now and then, and gesticulating all the time, they make slow progress, just 3 km/hr. When they finally reach home and she slams the door in his face without inviting him in, they have spent a total of 4 hours 15 minutes together since the time he picked her up. The extra 15 minutes, of course, were spent at the cinema, so we know that the actual walking took them 4 hours all combined.
What is the distance between the young woman’s home and the cinema?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 169.1
Hello Kabir,
For the coin to land cleanly inside the square without touching any of the edges, its centre should be away from each edge by a distance that is more than its radius. The diameter of the coin is 2cm, so it has to be at least 1 cm distant from all edges. So the area available to the coin inside the 3.5cm x 3.5cm square is a smaller square whose side is 3.5 – 2 = 1.5cm. The probability that the coin will land within the smaller square is: available area/total area = 1.5²/3.5² = 9/49.
— Dr Sunita Gupta, New Delhi
#Puzzle 169.2
Hi Kabir,
In the equation aᵇ x cᵃ = abca, the substitution is 2⁵ x 9² = 2592. So a = 2; b = 5; c = 9.
— Sabornee Jana, Mumbai
Solved both puzzles: Dr Sunita Gupta (Delhi), Sabornee Jana (Mumbai), Vinod Mahajan (Delhi), Shishir Gupta (Indore), Shri Ram Aggarwal (Delhi), Yadvendra Somra (Sonipat), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Amarpreet (Delhi), Professor Anshul Kumar (Delhi), Ajay Ashok (Delhi), YK Munjal (Delhi)
Problematics will be back next week. Please send in your replies by Friday noon to problematics@hindustantimes.com
