Call it a study in probability.
Fifteen-year-old Tajik schoolgirl Yosuman Ismonzoda says she stumbled on her ticket to international notoriety "completely by chance" when she took her younger brother to his afterschool activity.
"One day I sat in the back row waiting for my little brother to finish his mental-counting classes," Ismonzoda says. "It caught my attention immediately."
Soon she was hooked, and she's won seven gold medals in Tajik and regional contests since joining the classes less than a year ago.
The path of Manizha Toshboltaeva, also 15, might seem less unlikely on the surface.
She's the daughter of a founder of the Empire of Knowledge private learning center in Dushanbe, which has burnished its reputation with the girls' recent rise to whiz-kid status. But she insists that nothing was preordained.
"All other children were so fast in counting, and I couldn't keep up with them," Toshboltaeva recalls of deciding to learn mental arithmetic after losing a school competition. "When I came home from school, I told myself to learn everything."
Now they're counting their blessings and getting used to being recognized as mini-celebrities as "children ask us to take selfies together," according to Toshboltaeva.
They were thrust into the international spotlight after winning the GeniusKid 2017 contest in Moscow on November 4.
Ahead of that contest, they had appeared on a popular Russian TV show, Amazing People, where they showed off their talent at mental calculation -- adding, subtracting, and multiplying dozens of three-digit numbers against a stopwatch.
In each test, the teenagers came up with correct answers to standing ovations from the audience, many of whom shook their heads in disbelief.
The "genius" girls are used to people not believing them. "We get it a lot," Toshboltaeva says. "People tell us it's fake, or that we've been given the answers in advance. People test us, interview us to make sure."
The TV appearances and the GeniusKid victory drew praise in an official speech by Tajik President Emomali Rahmon.
Ismonzoda and Toshboltaeva returned home to a hero's welcome at Dushanbe International Airport on November 7, when government officials and dozens of young fans joined the girls' families and friends to greet them.
Nicknamed "Calculator" by her fans, Ismonzoda can count dozens of digits without pen or paper while reciting poetry at the same time.
On the Russian TV show, Toshboltaeva also displayed her unusual gift for correctly guessing the speed of passing vehicles, a skill that has earned her the nickname "Radar."
Creating 'Empire Of Knowledge'
Toshboltaeva says she "wasn't particularly interested in it in the beginning" but joined mental-arithmetic classes when the Empire of Knowledge was established in the Tajik capital by her mother, Veronika Korobkina, in March 2016.
With salesman-like assuredness, Korobkina insists that "any child is capable of learning to mentally count just like these two girls."
Korobkina, who has worked as a schoolteacher in Dushanbe for more than two decades, is credited with opening the first-ever mental-arithmetic classes in Tajikistan.
Teaching the technique is described by one of its teachers as "50 percent teaching math and 50 percent developing the logics, logical thinking, photographic memory, [and] focusing the attention."
Its teaching frequently employs an abacus before students graduate to imagining that they are using one -- responsible for the rapid hand and finger movements of users like Ismonzoda and Toshboltaeva.
In 2016, President Rahmon urged educators in post-Soviet Tajikistan, home to around 8 million people, to promote science among the younger generation, Korobkina says.
"After some research, I realized that we don't teach mental arithmetic in our country, so I decided to open the first such classes with the help of our partner, the Moscow-based Abacus school," she tells RFE/RL.
'Willing To Learn'
Located in the central Dushanbe, the Empire of Knowledge has dozens of students aged 6-15 who attend mental-counting classes twice a week, including Ismonzoda and Toshboltaeva.
The exposure has quickly boosted its profile among parents seeking to enroll their kids in special schools to give them a leg up on the competition in Tajikistan, where jobs can be hard to come by, or abroad.
"We are being flooded with phone calls from parents," Empire of Knowledge's director says.
The $50 course fee is significant in a country where monthly wages are around $150.
Korobkina says there are no admission tests or interviews for new students. "There is a theory that a certain child is not predisposed to learn languages or mathematics, and so on. It's an incorrect approach," she says. "The most important thing is the child's willingness and interest in learning."
Earlier this year, 13 students from the Empire of Knowledge's 15-member team medaled, including five golds, at the Central Asian Abacus and Mental Arithmetic Competition in Kyrgyzstan.
Ismonzoda and Toshboltaeva are expected to represent Tajikistan in several domestic and international contests in 2018. The teenagers say mental arithmetic has boosted their self-confidence in public appearances and sharpened their focus in other subjects, too.
Ismonzoda wants to continue studying mathematics at a "good university abroad." For Toshboltaeva, mental arithmetic will remain a hobby as she plans to pursue her interests in music and acting, "maybe in Los Angeles."