The cochlea is the marvellous structure in the inner ear that is shaped like a snail shell and transforms sounds into the nerve impulses that your brain can process and interpret. For decades, hearing experts thought that its spiral shape had no effect on how it functions. However, a recent study headed by Vanderbilt mathematician Daphne Manoussaki calls this conventional wisdom into question. She and her colleagues, Richard Chadwick and Emilios Dimitriadis of the National Institutes of Health, have created a mathematical model of the cochlea that finds the spiral shape acts to enhance the low frequency sounds that we use to communicate with one another. They published the results recently in the journal Physical Review Letters.
Here is a numbered list of statements, some true, some false, which refer to a specific number (positive integer, base 10). It just so happens that if a statement is true then its index number appears among the number’s digits, and if a statement is false then its index number does not appear among the number’s digits. Find the number.
The sum of the number’s digits is a prime.
The product of the number’s digits is odd.
Each of the number’s digits is less than the next digit (if there is one).
No two of the number’s digits are equal.
None of the number’s digits is greater than 4.
The number has less than 6 digits.
The product of the number’s digits is not divisible by 6.
The number is even.
No two of the number’s digits differ by 1.
At least one of the number’s digits is equal to the sum of 2 other digits. (Any of the digits may be equal, as long as all 3 digits are distinct.).
In the game of Letter Dice , a different letter of the alphabet is on each face of each of the 4 cubes, so that 24 of the 26 letters of the alphabet occur. Words are formed by rearranging and turning the dice so that the upward-facing letters spell a 4-letter word. The 13 words below have been anagrammed using today’s cubes, which do not have a Q or X on them. Can you find the 6 letters on each die?
BRAG; DAYS; DOZE; CLUB; CONK; FAUN; JERK; MAIL; PELT; POND; SHIP; VOTE; WANT
Solutions on October 16
CORRECT ENTRIES
September 18
Sisir Das, Cal-89; Subrata Kumar Chatterjee, Cal- 94; Amartya Chakraborti; Maharshi Ray; Sumita Garai; Arnab Kr Sadhukhan; Samagata Banerjee, Cal- 101; Rashmi Baid, Cal-40; Ankit Sanghai, cal- 7; Dipak Singh;Pankaj Bucha, Cal- 17; Subhendu Bikas Samanta, Howrah; Ranjan Sur Chaudhury, CAl- 112; Samir Maulick; Arnab Roy, Cal- 32; Joyee Pandit; K.Sengupta; Cal- 19; Ranjan Kumar Nandi,Durgapur; Kushal Mehta, Cal- 26; Ranjan Sur Chaudhuri
Please send in your entries to knowhow@abpmail.com, within 10 days.
PUZZLE CRACKED
The response to the puzzle this week (September 18) was overwhelming. Please continue to send your feedback to let us know if you are enjoying solving the riddles. Hope this festive season is full of fun and laughter for you all. Coming back to our brainstorming sessions, we now dislose the name of the person who has been able to crack the cubes-and-letters puzzle. Ranjan Sur Chowdhury was both methodical and logical in his approach. The solution sent by him is provided below.
Solution : The letters on the four dice of Letter Dice 7 (in order of recovery) are
PGIBJY
AURHCD
VSFOKM
ENXTWL
