Problematics | How to secure a crossword spot
The national crossword league follows a percentile system. Is there a safe cutoff that will guarantee a top-30 finish after 10 online rounds?
The Indian Crossword League, or IXL, is in progress. The second of 10 online rounds is currently live, with the subsequent rounds due every Sunday. The competition will end with a live contest in December among the 30 toppers of the online rounds.
The method of scoring in the online rounds carries the unmistakable promise of a puzzle. Points based on a percentile basis are awarded to the participants. You need to mind both your accuracy and your time. The earliest all-correct entrant goes to the top of the leaderboard with 100 points, the second one gets 99, and so on until every all-correct entrant has been accounted for. Say there are 70 of them. No #71 on the leaderboard, say with one mistake, is the earliest one to submit among those who made one mistake each. No #71 may have submitted earlier than No #70, or even earlier than No #1, but that single mistake means that he or she must appear below everyone who has submitted their entry without a mistake.
I was No #27 on the leaderboard after the first round, and hence have 74 points. If I finish at #100 in the second round, I will get 1 point for that round, taking my total to 75 points after two rounds. Points are thus accumulated over the 10 rounds.
Those were the basics. The key question I am wondering about is whether there is a “safe score” that guarantees you a place among the top 30 after the 10 online rounds.
#Puzzle 161.1
As regular puzzlers, Problematics readers will have observed that any participant’s position and score always add up to 101 in any given round. No #1 has 100 points, No #2 has 99, No #27 has 74, and No #100 has 1 point.
Thus No #30 in any round has 71 points. If the same players occupy the same positions in the top 30 over the entire 10 weeks, No #30 will finish with 71 x 10 = 710 points. That makes 710 the cutoff score for qualification — provided that each one in the top 30 maintains an identical score and retains the same position, round after round after round.
Real life, however, does not work like that. A player between positions #25 and #30, say myself, can do poorly in the second round and drop out of the top 30 in the overall leaderboard. In the third round, the same player may do exceptionally well and inch back into the lower ranks of the top 30 on the overall leaderboard. By then, the composition of the top 30 will have changed. Some leaders will have swapped positions, some will have fallen into the #30-40 bracket, and some new ones from below will have entered the top 30. In short, the scores of the top 30 will likely no longer be in arithmetic progression.
In such a dynamic scenario, is there really a safe cumulative score that will ensure a place in the top 30 after the 10 online rounds. Try to solve this without going into higher branches of mathematics, if that’s possible.
#Puzzle 161.2
Using each of the digits 0-9 once, find one or more 10-digit numbers that are divisible without remainder by all numbers between 2 and 18 inclusive.
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 160.1
The answer to the library puzzle is that Poirot will read War and Peace, Hastings will read Anna Karenina, and Miss Marple will read Resurrection. A simple process of elimination satisfies all the conditions. There is probably a matrix method one could employ, but I found it easier to use trial and error.
— Dr Jeffrey Geist, Columbus, Ohio
(I would shudder at the idea of anyone using a matrix to solve a puzzle as simple as this, Dr Geist, and thankfully no reader has gone in that direction. Thank you for your first attempt at Problematics. — Kabir)
#Puzzle 160.2
Hello Kabir,
Last year (2024) is the answer to the calendar puzzle. It had 7 dates that satisfy the condition described: 24/1/24, 12/2/24, 8/3/24,6/4/24, 4/6/24, 3/8/24, and 2/12/24. By the way, this will be true in every century.
— Sanjay Gupta, New Delhi
Solved both puzzles: Sanjay Gupta (Delhi), Vinod Mahajan (Delhi), Shishir Gupta (Indore), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Dr Sunita Gupta (Delhi), Professor Anshul Kumar (Delhi), Ajay Ashok (Delhi)
Solved #Puzzle 160.1: Dr Jeffrey Geist (Columbus), Yadvendra Somra (Sonipat)
Solved #Puzzle 160.2: YK Munjal (Delhi)
(For the record, Yadvendra Somra has sent an alternative solution to Puzzle #159.1 that is different from the two versions published last week. He had solved the puzzle correctly last week itself, but made a typo in the mail he sent me. — Kabir)
Problematics will be back next week. Please send in your replies by Friday noon to problematics@hindustantimes.com
