Problematics | The rate of sending and cancelling an invitation
Are there enough equations to determine the variables? You may need to think out of the box to solve this puzzle, partly inspired by a 150-year-old classic.
From a setter’s perspective, there are four kinds of puzzles. The most satisfying ones are the setter’s own creations, for example, my Gabbar Singh puzzle in Week 50. The other three kinds derive from the work of other setters: puzzles reproduced as is with due credit, old puzzles adapted into a new form, and brand-new puzzles inspired by an existing original.
The following puzzle belongs to the last category. It is my own, inspired by a 150-year-old classic.
The ring of the mobile had drowned one of her words, which, as you will have deduced, was a number denoting an hour of the clock. Her husband took the call, listened, and made a face. “She’s not coming,” he said, handing her the phone.
They chatted with their daughter for some time. The invitations her parents had just finished sending (the first lot by text, and then the rest by mail) were for her planned homecoming party.
Once the call ended, the mother sighed. “Nothing to do but mail or text everyone that the party’s off,” she said. This time, they wrote the cancellation mails first, starting exactly 15 minutes after they had finished sending the last of the invitations.
“The mails take longer,” she said. “Four cancellation mails between us in an hour, the same rate at which we had mailed the invitations to the same guests.”
“The text messages will be faster,” her husband replied. “Remember, we had texted the invitations to that lot of guests @6/hour.”
Alas, it was not to be. Relatives and friends responded to the cancellation texts with so many questions and subsidiary questions that the parents managed to text only 3 cancellations every hour.
When the last message had been texted, the mother looked at the time again. “12:15 am. What a waste of a day.”
How many invitations did they send by mail, and how many by text, before cancelling them all?
Take all 10 digits from 0 to 9. Using each digit exactly once, write two fractions whose sum is 1.
Mailbox: Last week’s solvers
Hi Kabir Sir,
Let the tops of the 3 dice be x, y and z. Adding: x + y + z.
Let the dice x and y be picked and therefore the bottom faces will be (7 – x)* and (7 – y)* respectively. Adding: x + y + z + (7 – x) + (7 – y) = 14 + z
After these 2 dice are rolled again, let the spots on their top faces be a and b. Adding: 14 + z + a + b
Picking up a, spots on the bottom will be (7 – a)*. Adding: 14 + z + a + b + (7 – a) = 21 + z + b
Rolling the same die again, we get w as the top face. Adding: 21 + z + b + w
Therefore, when the smart alec turns around, he adds the total on the top faces of the three dice and adds an extra 21.
— Ananya Arvind, DPS Vasant Kunj, Delhi
*What Ananya left unsaid: in a standard die, the spots on any two opposite faces add up to 7.
Solved both puzzles: Ananya Arvind (DPS Vasant Kunj), Dr Sunita Gupta (Delhi), Amardeep Singh (Meerut), Harshit Arora (IIT Delhi), V Anand (Noida), Prof Anshul Kumar (Delhi), Malay Mittal (Delhi), Sunita & Naresh Dhillon (Gurgaon), Dr Nakul Makkar (Noida), Charvi Brajpuriya (Faridabad), Group Capt RK Shrivastava (retd; Delhi), Vardan Bhaskar (Modern DPS-89, Faridabad), Vinod Mahajan (Delhi), Ajay Ashok (Mumbai), Yadvendra Somra (Sonipat), Shri Ram Aggarwal (Delhi), Abhishek Garg (Chandigarh)
Solved #Puzzle 55.1: Bhaskar Mundhra (Ghaziabad), Bhuvi Jain (Delhi), Rachna Jain (Delhi), Radhika Joshi (DPS Vasant Kunj), Arun Kumar Gupta (Greater Noida), Vivek Aggarwal (Bangalore), Shishir Gupta (Indore), Satishwar (Delhi), Saksham Bhatnagar, Joydeep Mahato
Solved #Puzzle 55.2: Sanghamitran Rajan (BVN Delhi), Shriyon Bhattacharya (Delhi), Parul Kohli
Problematics will be back next week. Please send in your replies by Friday noon to firstname.lastname@example.org