E-Paper
Problematics | Word multipliers
This week, fill up a crossword on the basis of a numerical key, and hunt for a number with two properties
The last time we had a numerical word puzzle of this kind, a number of readers wrote back to say it was a tough one. I expect this week’s revival (same kind, different words and numbers) will also be tough, which is why the word-number puzzle comes before the one that is strictly numerical.
We had discussed the rules the last time, but I am repeating them for the benefit of new readers.
#Puzzle 173.1
The crossword grid contains common words, selected carefully to give you a numerical solving experience rather than go dictionary hunting. There are no clues with word meanings, but the “products” of the letter values of the words. The key is A = 1, B = 2, C = 3 etc up to Z = 26. “Product” means simply the product of all the letter values of a word, e.g. the product of HAT = 8 x 1 x 20 = 160.
The products in the above grid are: 3 Across = 106920, 5 Across = 11781, 8 Across = 2808, 9 Across = 1050, 10 Across = 5400, 11 Across = 5320, 12 Across = 18480, 1 Down = 31536960, 2 Down = 604800, 4 Down= 743820, 5 Down = 124950, 6 Down = 320760, 7 Down = 1320000.
See if you can fill up all the letters.
#Puzzle 173.2
A triangular number is one that represents the dots in an equilateral triangle formed by placing 1 dot in the first row, 2 in the second row and so on. So, 10 is a triangular number with four rows containing 1, 2, 3 and 4 dots, and each row representing a length of 4. The smallest triangular number, 1, is also a perfect square. For the next perfect square, you have to go up to 1 + 2 + 3 +… + 8 = 36.
Which is the next such perfect square among triangular numbers after 36?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 172.1
Hi Kabir,
Suppose the couple starts at an initial speed of S kph. Their speed after the breakdown and repair is given to be 30 kph. The husband's journey time is 1/4 hours (8:30 pm – 8:15 pm) less than that of his wife. This time is gained because for a distance of 30 km between the two breakdown spots, he drives at speed S kph while his wife drives at 30 kph, other times remaining the same.
Therefore, (30 km / 30 kph) – (30 km / S kph) = 1/4 hour, giving S = 40 kph.
The breakdown of the wife's car happened 2 hours after the start of the journey. Therefore, the distance of this breakdown spot from her home is 40 kph x 2 hours = 80 km.
Suppose the distance between the spot where the husband's car broke down and the destination is D km. He lost 1/4 hour (8:15 pm – 8:00 pm) because of slower driving over this distance (30 kph instead of 40 kph) and 10 min (= 1/6 hour) spent in repair.
Therefore, (D km / 30 kph) – (D km / 40 kph) + 1/6 hour = 1/4 hour, giving D = 10 km.
The length of the journey = 80 km + 30 km + 10 km = 120 km.
The breakdown spots are at distances of 80 km (wife's car) and 110 km (husband's car) from their home.
— Professor Anshul Kumar, New Delhi
#Puzzle 172.2
Hello Kabir,
I think we can find out which one is the magnet. There are at least two methods. Although the room is empty, maybe we can find some string and suspend each rod. The magnet will align itself towards north and south while the iron bar will be oriented randomly.
In the second method, take bar 1 and place its end at the centre of bar 2. If the attraction is strong, bar 1 is the magnet. If it doesn't stick (or attraction is weak), bar 2 is the magnet, because at the centre of a bar magnet the magnetic power is almost zero.
— Dr Sunita Gupta, New Delhi
Solved both puzzles: Professor Anshul Kumar (Delhi), Dr Sunita Gupta (Delhi), Dr Jeffrey Geist (Columbus, Ohio), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Shishir Gupta (Indore), Ajay Ashok (Delhi), Yadvendra Somra (Sonipat), Vinod Mahajan (Delhi), YK Munjal (Delhi), Shri Ram Aggarwal (Delhi)
Solved Puzzle 172.1: Nitin Trasi (Sydney)
Solved Puzzle 172.2: Anil Khanna (Ghaziabad), Dr Vivek Jain (Baroda)
