A 9-digit number, divisible by 9, is my password to a secret account where I store my puzzles. The digits 1 to 9 each appears once. Remove the last digit and the 8-digit number is divisible by 8. Remove the last digit again and the 7-digit number is divisible by 7. And so on, until the last digit.

I will need to change my password after you figure it out. But what is it?

#Puzzle 16.1:

Hello Kabir,

The Jamnagar wala would have counted 119 days and nights.

A division of 39,600 km by 330 km/day gives us 120 days. The birds flying east will see 120 sunsets. However, their days will be shorter than for our man in Jamnagar. As the days progress, the shortfall will accumulate. By the time the birdies get back home, they would have slept for 120 nights, while the Jamnagar wasi would have slept for only 119 nights.

PS: Reminds me of Around the World in 80 Days, Jules Verne, 1872.

— Sanjay Gupta, Delhi

330 km out of a 39600-km circumference means (330*24*60)/39600 = 12 minutes.

Since the birds are flying east, they gain 12 minutes daily. Hence, they would gain 120 x 12 = 1440 minutes = 1 day in their journey around the Earth.

Hence, the total days elapsed will be 1 day less than 120 days, which is 119 days.

— Vinod Mahajan, Delhi

#Puzzle 16.2:

Let the time required for the first half be 2t and for the third and fourth quarters, t each. Then 3t = 67 minutes 30 seconds, and the total time, 4t = 90 minutes.

— Gopal Menon, Mumbai

Solved both puzzles: Naresh Dhillon (Gurgaon), Gopal Menon (Mumbai), Sanjay Gupta (Delhi), Biren Parmar (Bay Area, California), Vinod Mahajan (Delhi), Amardeep Singh (Meerut)

Solved #Puzzle 16.2: Varsha Jain (Mumbai), Shivika Gupta (Delhi), Kshitij Kumar (Delhi), Jayant Jogaikar, Rajesh Haridas Asher, Satishwar Juneja (Delhi), Sudesh Dogra (Delhi), Rahul Agarwal (Bay Area, California), Natrajan (Bangalore), Jaikumar Bhatia (Ulhasnagar, Thane), Jasvinder Singh (Nabha), Ajay Ashok (Mumbai)

Figuring #Puzzle 16.1:

There was a typo in the print version last week, but that is not the reason so many got #Puzzle 16.1 wrong. The circumference of the Earth should have read 39,600 km, not 39,600 m. Most readers noted this and proceeded with km.

An error many readers did make, however, was in not factoring in the rotation of the Earth. In Around the World in 80 days, Phileas Fogg, circuiting the Earth from east to west, sees 80 new sunrises in 79 real days. Jules Verne explains it by using longitudes: Fogg gains 18 minutes between every two sunrises.

You can also solve it without calculating the time saved on each section. If you go eastward around the Earth and see the sun rise and set 120 more times, it means a stationary observer will have seen it rise and set 119 times. If you go east to west and see 120 new sunrises and sunsets, a stationary observer would see 121 of both.

The birds count their 120th sunset on arrival in Jamnagar, and their 120th sunrise the following morning. That is the 119th sunrise for the Jamnagar resident.