The 9th Mental Calculation World Cup has just taken place on the weekend of the 16th July 2022, organised by Ralf Laue. Many of the competitors had met before at the World Cup or at other international events, but others made their debut here. Congratulations to everyone involved!
Personally, I would have loved to be there but I had too many commitments already scheduled, so I had all the FOMO from the UK. Many thanks to Mohammad El-Mir, Andy Robertshaw, Freddis Reyes, Jan van Koningsveld and Boris Quach for keeping me updated! If you note anything that needs correcting or adding, please contact me here.
Combined Awards
Overall Winners: for the combined score of all 10 events
- 1st: 🇮🇳 Aaryan Shukla: 604.33 points (age 12!)
- 2nd: 🇯🇵 Ono Tetsuya: 559.45 points
- 3rd: 🇱🇧 Mohammad El-Mir: 542.19 points
Most Versatile Calculator: for the combined score of the 5 surprise tasks only.
- 1st: 🇯🇵 Ono Tetsuya: 308.26 points
- 2nd: 🇯🇵 Naoto Higa: 306.11 points
- 3rd: 🇧🇬 Kaloyan Geshev: 265.44 points
Individual Events
The competition contained 10 rounds: 4 standard events, 1 special challenge that was announced in May, and 5 surprises that were announced during the competition itself, so competitors had to improvise a method.
Calendar: Calculate the weekday for as many dates as possible in one minute. Dates are randomly chosen between years 1600-2099. Akshita set a new world record for calendar calculations on paper! Here’s the human calendar algorithm for those of you who would like to learn.
- 1st: 🇮🇳 Akshita Shah: 80
- 2nd: 🇩🇪 Jan van Koningsveld: 57
- 3rd: 🇩🇿 Hakim Belouad: 56
Addition: Add together sets of ten 10-digit numbers. You have to solve as many questions as possible in 7 minutes. 1 point is deducted for every wrong answer, although Naoto managed to solve all questions with zero errors! Ono set a new world record for additions on paper!
- 1st: 🇯🇵 Ono Tetsuya: 34 correct (32 points)
- 2nd: 🇯🇵 Naoto Higa: 31 (31)
- 3rd: 🇮🇳 Aaryan Shukla: 31 (29)
Multiplication: Multiply two 8-digit factors, such as 12345678 × 98765432. You have to solve as many questions as possible in 10 minutes. 1 point is deducted for every wrong answer. Most competitors use some form of criss-cross multiplication.
- 1st: 🇮🇳 Aaryan Shukla: 23 correct (21 points)
- 2nd: 🇺🇸 Samuel Engel: 23 (19)
- 3rd: 🇮🇳 Mishti Shah: 19 (17)
Square roots: Extract the root of a 6-digit number, to 8 significant figures of accuracy. You have to solve as many questions as possible in 10 minutes. 1 point is deducted for every wrong answer. All three competitors smashed the world record for square roots calculations on paper, with Aaryan the new fastest.
- 1st: 🇮🇳 Aaryan Shukla: 79 correct (74 points)
- 2nd: 🇧🇬 Kaloyan Geshev: 59 (47)
- 3rd: 🇮🇳 Granth Thakkar: 54 (44)
Challenge task: several questions of this type, as announced a few months previously. Due to the high difficulty of this task, where no points were available for partially-correct answers, only 2 competitors scored above 0 points!
I briefly looked for an efficient strategy that generates the answer digit-by-digit by combining the following algorithms for square roots and arbitrary divisions, but didn’t finish. If someone can demonstrate a proper implementation, I would be curious to know! You can always contact me by email. Otherwise it can be done in two stages, perhaps using a mnemonic technique to remember the intermediate result.
- 1st: 🇱🇧 Mohammad El-Mir & 🇮🇳 Aaryan Shukla: 2 correct
- 3rd: everyone else including you 🙂
Surprise #1: This was a combination of additions and multiplications, such as 3 × 6011594 + 4 × 1855235 + 5 × 2805164 + 6 × 6188748 + 7 × 2811490. My suggestion would be to solve this digit-by-digit, starting with 3×4 + 4×5 + … + 7×0.
🇺🇸 Samuel Engel achieved the top score (29 correct), narrowly followed by 🇯🇵 Ono Tetsuya, and 🇨🇺 Freddis Reyes and 🇯🇵 Naoto Higa on joint 3rd.
Surprise #2: These were exact divisions, of the form 43043645 ÷ 8815. These can be solved using the division method linked above, or by subtracting multiples of the divisor (8815).
There was a very tight race for top place, with 🇧🇬 Kaloyan Geshev on 76, 🇮🇳 Aaryan Shukla on 75, 🇱🇧 Ahmad Chhimi and 🇯🇵 Ono Tetsuya on 74.
Surprise #3: Here the challenge was to compare two powers—a simple example would be 22^11 and 13^14. This can be solved in many ways—the fastest is probably by estimating the logarithms 11 log 22 < 14 log 13.
🇮🇳 Akash Rupela won this round, with 🇺🇸 Samuel Engel, 🇮🇹 Michelangelo Sabatini and 🇩🇪 Martin Drees tied for 2nd place.
Surprise #4: This estimation exercise asked competitors to estimate the value of, for example 4754 ÷ √364 to the nearest integer. This is similar to the challenge task, but easier as many fewer digits of accuracy are required.
🇯🇵 Naoto Higa had the highest score, while 🇱🇧 Mohammad El Mir and 🇯🇵 Ono Tetsuya came joint second.
Surprise #5: The final task was the square of a product, such as √(592 × 1665 × 720), where the answer is guaranteed to be an integer. I would solve this by partially factorizing the product and collecting square factors.
This was won jointly by 🇮🇹 Domenico Mancuso and 🇧🇬 Kaloyan Geshev, while 🇱🇧 Mohammad El Mir came 3rd.
Hectoc Competition
Hectoc is a number game where you have to combine six digits 1–9 in order, to make the number 100.
Although not part of the official competition, there was a separate Hectoc tournament, with a clear winner! Correct answers scored one point, while incorrect answers scored –0.5 points.
- 1st: 🇧🇬 Georgi Georgiev (25.5)
- 2nd: 🇬🇧 Andy Robertshaw (18)
- 3rd: 🇩🇪 Elke Kuge, 🇩🇪 Joshua Spring and 🇩🇪 Bernhard Clasen (17.5)
Record Attempts
Several world records were broken during the event! This was separate to the main competition.
- Square roots: Granth Thakkar (10 tasks in 47.73 seconds)
- Multiplication of two 20-digit numbers: Aaryan Shukla (a task in 1 minute 45 seconds)
- Multiplication of two 5-digit numbers: Aaryan Shukla (10 tasks in 56.79 seconds)
- Exact division of 10 digits by 5 digits: Aaryan Shukla (10 tasks in 41.62 seconds)
Other Announcements:
The competition was generously supported by the Andreas Mohn Foundation and hosted by the Heinz Nixdorf MuseumsForum in Paderborn, Germany.
The next top-level competitions will be:
- Mind Sports Olympiad (World Championship) in London—August 24–25 (announcement soon!)
- The Junior Mental Calculation World Championship in Bielefeld, Germany, October 1–2 (registrations closed!)