Composers often speak of fitting chords and melodies together, as though sounds were physical objects with geometric shape — and now a Princeton University musician has shown that advanced geometry actually does offer a tool for understanding musical structure, reports ScienceDaily. An attempt to answer age-old questions about how basic musical elements work together, Dmitri Tymoczko has journeyed far into the land of topology and non-Euclidean geometry, and has returned with a new — and comparatively simple — way of understanding how music is constructed. His findings have resulted in the first paper on music theory that the journal Science has printed in its 127-year history, and may provide an additional theoretical tool for composers searching for that elusive next chord.

PUZZLE 1. At Widgett, Inc., the pecking order of executives under CEO Norm Bates is easily determined: each senior executive has an office on a different floor 5th-9th of company headquarters, below the CEO’s 10th floor spaces; and the closer to the 10th floor an executive works, the more in favour he or she is. Last week, the offices of the five senior executives, including the VP for Marketing, were swapped, signalling a power shift in the company. Given the data below, can you solve this tricky Logic Puzzle by determining who was on each floor before the move and who is there now: each executive’s full name (one first name is Richard, one surname Dubois) and his or her position at Widgett, Inc.?

Three of the five senior executives saw their power diminish as they moved down in the building, one dropping three floors; the two who gained power moved up three and two floors.

Feldman didn’t occupy the 7th floor office before the power shift.

The Chief Information Officer moved up in the building to the suite vacated by Blocker.

The VP for sales moved into the Chief Financial Officer’s old spaces.

Hazlett was moved down one floor in the shake-up, with Linda taking over Hazlett’s office.

Alice got Grayson’s former suite, while Grayson moved into the office vacated by the VP for Human Resources. Both Alice and Grayson have seen their power diminish as they are assigned to lower floors than before.

Michael left a pen set behind as a gift for Larry, who moved into Michael’s old office.

The executive who had the 9th floor office before the power shift didn’t end up on the 8th floor afterwards

Solutions on September 11

CORRECT ENTRIES

August 14

Sayonil Mitra, Shantiniketan; Shradha Chopra, Calcutta; K. Sengupta; Siddhart Udani, MCKV Institute for Engineering; Suman Chattopadhyay, Ranchi; Diptiman Banerjee, Durgapur; Kalyani Banerjee, Jamshedpur; Anil Goswami, Guwahati; Anirudh Pal, Shantiniketan; Ayan Mukhopadhyay, Sodepur; Sunil Mitra, Noida; Anil Gupta, Calcutta; Shayan Chattopadhyay, Calcutta; K. L. Mukherjee, Jamshedpur; Piyali Mukherjee; Somnath Shukla, Calcutta

PUZZLE CRACKED

The response this week (August 14) was overwhelming. Let me know whether you people are enjoying solving the puzzles. Please don’t send your solutions as an attachment. And don’t forget to mention the date of the puzzle in the subject of your email. The solution to the puzzle is given below.

Solution: During the thanksgiving dinner, the Pilgrim families swapped their livestock while playing the game in the following manner: The Allertons traded Kate, the goat, for Prissy, the sheep.

The Brewsters traded Molly, the cow, for Kate, the goat.

The Hopkinses traded Annie, the horse, for Bessie, the pig.

The Mullinses traded Bessie, the pig, for Molly, the cow.

And the Whites traded Prissy, the sheep, for Annie, the horse.