The 10th Mental Calculation World Cup (official website) has just taken place on the weekend of the 14th September 2024, organised by Ralf Laue. Many of the competitors had met before at previous World Cups or at other international events, but others made their debut here. Congratulations to everyone involved!
Note: if you note anything that needs correcting or adding, please contact me here.
From 16 countries, 35 mental calculators worldwide competed in this event, and also enjoyed various meals together as well as a visit to the world’s largest computer museum. The youngest competitor is 🇰🇬 Aidarbek Kubanychbekov (age 10) and the eldest is 🇳🇱 Willem Bouman (age 84).
Combined Awards
Overall Winners: for the combined score of all 9 events
- 1st: 🇮🇳 Aaryan Shukla: 819.84 points (age 14—who also won in 2022)
- 2nd: 🇧🇬 Kaloyan Geshev: 532.86 points (also age 14)
- 3rd: 🇯🇵 Hiko Chiba: 455.75 points
Most Versatile Calculator: for the combined score of the 5 surprise tasks only.
- 1st: 🇮🇳 Aaryan Shukla: 419.84 points
- 2nd: 🇧🇬 Kaloyan Geshev: 383.33 points
- 3rd: 🇯🇵 Hiko Chiba: 282.39 points
Individual Events
The competition contained 9 rounds: 4 standard events 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. Aaryan 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: 🇮🇳 Aaryan Shukla: 100
- 2nd: 🇩🇿 Hakim Belouad: 62
- 3rd: 🇩🇿 Walid Henni: 61
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 Hiko managed to solve 20 questions with zero errors! Swanand and Aaryan later set world records for additions using the Memoriad software.
- 1st: 🇮🇳 Aaryan Shukla: 34 correct (29 points)
- 2nd: 🇮🇳 Mishti Dharmesh Shah: 23 correct (22 points)
- 3rd: 🇮🇳 Swanand Bhore: 24 correct (20 points)
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: 28 correct (25 points)
- 2nd: 🇮🇳 Mishti Dharmesh Shah: 21 correct (17 points)
- 3rd: 🇯🇵 Hiko Chiba: 16 correct (17 points)
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. Both Aaryan and Kaloyan beat their scores from when they won the same medals in MCWC 2022. Kaloyan and Aaryan later set world records for square roots using the Memoriad software.
- 1st: 🇮🇳 Aaryan Shukla: 86 correct (82 points)
- 2nd: 🇧🇬 Kaloyan Geshev: 69 correct (61 points)
- 3rd: 🇮🇳 Akash Rupela: 27 correct (26 points)
For each of the 5 surprise categories, 10 minutes were available to solve it.
Surprise #1: Many tasks of the form –(27 × 32) + (24 – (34 × 28)) – ((43 × 12) – (65 × 95)) were set.
🇮🇳 Aaryan Shukla calculated all 30 questions correctly, while 🇯🇵 Hiko Chiba was close with 29 correct! 🇧🇬 Kaloyan Geshev was 3rd-most successful, with 25 correct.
Surprise #2: Many tasks were given of the form \(\frac{10}{30} + \frac{15}{88} + \frac{7}{24} = \frac{}{44}\), where the missing numerator is guaranteed to be an integer. These can generally be solved quickly by simplifying fractions, adding them in pairs and simplifying again.
🇮🇳 Aaryan Shukla (36 correct) had the highest score by far, followed by 🇮🇹 Domenico Mancuso (20 correct) and 🇧🇬 Kaloyan Geshev (18 correct).
Surprise #3: The challenge was to calculate \(\frac{\sqrt{1985}}{\pi}\) to as many significant digits as possible. The most successful strategy was to calculate \(\sqrt{1985}\) to 7–8 significant digits, memorize it, and then use a division algorithm to divide it by \(\pi\) to the same number of significant digits. 🇩🇿 Manar Benmasotra used the method of loci so she could memorize the first 20 digits of \(\sqrt{1985}\) without writing it down.
🇧🇬 Kaloyan Geshev and 🇮🇳 Aaryan Shukla both calculated the first 6 digits correctly, while 🇲🇾 Hua Wei Chan calculated 5 digits correctly.
Surprise #4: Each task was the difference of two products of 5-digit numbers, such as (13579 × 86420) – (31415 × 27182). The most successful strategy was to modify the criss-cross method: for each digit, adding on the terms from the left product then subtracting the terms from the right product and taking care with any negative totals.
This task proved very difficult, with only 🇫🇷 Boris Quach and 🇬🇧 Andy Robertshaw solving two questions correctly!
Surprise #5: The final task was to select the largest number from a given root, power and fraction. For example, \(\sqrt[4]{3888}\), \(1.966^3\) and \(\frac{2222}{277}\)
🇧🇬 Kaloyan Geshev again had the top score, with 63 marks (32 correct), while 🇮🇳 Aaryan Shukla and 🇯🇵 Hiko Chiba came 2nd and 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, where 40 fairly difficult problems were set.
- 1st: 🇧🇬 Georgi Georgiev (36)
- 2nd: 🇩🇪 Tina Bauer (36)
- 3rd: 🇩🇪 Bernhard Clasen (35)
World Record Attempts
Several world records were broken during the event! This was separate to the main competition. These were all achieved using the Memoriad competition software. [Note: please do not regard this article as an official source of calculation records—you will find official lists on recordholders.org]
The result was a dramatic battle as some of the world’s top calculators tried to break and re-break each other’s records. Maybe there will be further records at Memoriad 2024, or at the next Mental Calculation World Cup?
Addition of ten 10-digit numbers. This record was previously held by Jeonghee Lee, and was beaten three times over the weekend:
- by 🇮🇳 Aaryan Shukla in 96.39 seconds (for 10 of these 10 × 10 addition tasks), during a live show
- by 🇮🇳 Swanand Bhore in 88.40 seconds
- by 🇮🇳 Aaryan Shukla just eight minutes after his record had been broken(!) with a time of 78.08 seconds
Division of 10-digit numbers by 5-digit numbers, where the answer is guaranteed to be an integer. This was previously held by Aaryan Shukla (10 tasks in 41.62 seconds)
- by 🇧🇬 Kaloyan Geshev in 37.74 seconds
- by 🇧🇬 Kaloyan Geshev in 32.38 seconds
Square roots of 6-digit numbers (not perfect squares) to 8 significant digits. This was previously held by Granth Thakkar (10 tasks in 47.73 seconds)
- by 🇧🇬 Kaloyan Geshev in 42.77 seconds
- by 🇮🇳 Aaryan Shukla in 33.78 seconds
Public Show of Mind Sports
The public was invited to the Heinz Nixdorf MuseumsForum to see a show presented by some of the participants in the show:
- 🇧🇬 Kaloyan Geshev quickly calculated various square roots to 5 decimal places.
- 🇬🇧 Daniel Timms (me) memorized 100 binary digits in about 100 seconds.
- 🇩🇪 Johanna van Koningsveld calculated 62 calendar dates correctly in one minute.
- 🇲🇾 Hua Wei Chan quickly divided 6-digit numbers by 3-digit numbers, to many decimal places.
- 🇳🇱 Roger Roelofsma showed how he can count the letters in very long Dutch words almost instantly.
- 🇮🇳 Aaryan Shukla demonstrated flash anzan: addition of numbers up to 5 digits flashed rapidly on a computer screen. He then broke the world record for addition of ten 10-digit numbers.
- 🇮🇳 Akash Rupela solved several Rubik’s cubes, including one using only one hand, one while blindfolded, and a 4×4 cube.
Other Announcements:
The competition was generously supported by the Andreas Mohn Foundation and hosted by the Heinz Nixdorf MuseumsForum in Paderborn, Germany.
The remaining international competitions this year include:
- The Junior Mental Calculation World Championship in Bielefeld, Germany, September 21–23
- The Global Mental Math Olympiad in Dubai, October 26—27 (mostly for children)
- Memoriad in Dubai, November 06–10
- The GMCA League—Season 2, online for several months starting in October
And of course we hope to see the Mental Calculation World Cup return in 2026!