Problematics | What to wear to be allowed into a club
A club spells out who is allowed in; can you figure out who isn’t? There’s also a fun pun this week
Years of puzzling with readers have taught me that you cannot always predict whether a given puzzle is going to prove easy or tough for solvers. Last week’s puzzle on shared birthdays is a case in point. I thought it was going to be mildly challenging but ultimately gettable — which is the kind this column always aims at — but quite a few readers have got it wrong.
One of the puzzles this week, too, is meant to be in the mildly-challenging-but-ultimately-gettable category, while the other one is deliberately presented as a sitter. As usual, however, it’s ultimately the replies from readers that will tell us what was easy and what was hard.
A club with strict entry rules prefers to spell out who is allowed, rather than who isn’t. Only the following can enter:
* Men with long hair
* Women over age 25
* Men under age 25
* Under-25s who are not wearing jeans and are accompanied by a partner
* Under-25s wearing jeans and not accompanied by a partner
* Under-25s with long hair and not accompanied by a partner
* Short-haired men over age 25
* Short-haired under-25s who aren’t wearing jeans and aren’t accompanied by a partner
Who is not allowed?
The next one is such a sitter that it will be surprising if anyone fails to get it; it’s meant for laughs rather than to challenge anyone:
Once upon a time, a boy in a snowy land went out kayaking in a blizzard. His mother tried to dissuade him, but he wouldn’t listen. He should have, because his kayak froze in ice.
The boy managed to drag the frozen chunk back home and tried to melt the ice with the fire from a stove. His mother warned him how risky that was, but he wouldn’t listen. He should have, because the kayak burst into flames — and the boy, into tears.
“No use crying now,” his mother ticked him off. “You can’t heat your kayak and have it too.”
Those were momentous words. They were passed down from generation to generation, and eventually got lost in translation.
What is the modern-day version of the mother’s words?
Mailbox: Last week’s solvers
To calculate the probability of at least 2 people out of 22 sharing the same birthday, we'll calculate the probability that none of them share a birthday, and then subtract that from 1. The first person can have any birthday (365/365), probability of the second person having a different birthday is (364/365), probability of the third person having a different birthday from the first two is (363/365), and so on. Probability of at least 2 people out of 22 sharing a birthday = 1 – [(365/365) * (364/365) * (363/365) * ... * (344/365)] ≈ 0.4751, or a 47.51% (rare, < 50%).
To get the minimum number of people so that the probability of at least 2 sharing a birthday is 50% or more, I use the same approach with 23 people. Probability = 1 – [(365/365) * (364/365) * (363/365) * ... * (343/365)] ≈ 0.5073 or 50.73%. So, there is more than a 50% chance that at least 2 people out of 23 will have the same birthday.
— Dr Nakul Makkar, Noida
Other similar equations are:
134 x 29 = 58 x 67 146 x 29 = 58 x 73
158 x 32 = 64 x 79 174 x 23 = 58 x 69
174 x 32 = 58 x 96 259 x 18 = 63 x 74
532 x 14 = 76 x 98 584 x 12 = 96 x 73
— Amardeep Singh, Meerut
Solved both puzzles: Dr Nakul Makkar (Noida), Amardeep Singh (Meerut), Sunita & Naresh Dhillon (Gurgaon), Dr Sunita Gupta (Delhi), Shruti M Sethi (Ludhiana), Harshit Arora (Delhi), Akshay Bakhai (Mumbai), Shri Ram Aggarwal (Delhi), Ajay Ashok (Mumbai), Vivek Aggarwal (Bangalore), Sandeep Bhateja (Hoshiarpur), Prof Anshul Kumar (Delhi)
Solved #Puzzle 48.1: Y K Munjal (Delhi), Saurish Seksaria (Navi Mumbai)
Solved #Puzzle 48.2: Khushboo Yadav (Faridabad), Gaurav Gummaraju (Navi Mumbai), Prakash Bhate (Mumbai), Shishir Gupta (Indore), Vinod Mahajan (Delhi), Jawahar Lal Aggarwal (Vasundhara, Ghaziabad), Jaikumar Bhatia & Disha Bhatia (Ulhasnagar, Thane), Jaya Lohani, Kinjal Sanghrajka, Satvik Sindhav, Asha Nanda, Padmakumar.
Problematics will be back next week. Please send in your replies by Friday noon to firstname.lastname@example.org