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Fundamentalnaya i Prikladnaya Matematika, 2020, Volume 23, Issue 3, Pages 37–47
(Mi fpm1897)
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A hundred from a bus ticket
V. V. Borisenkoa, R. Rakhmatovb a Lomonosov Moscow State University, Moscow, Russia
b Branch of Lomonosov Moscow State University in Dushanbe, Dushanbe, Tajikistan
Abstract:
We consider the comic task of obtaining the number $100$ from a six-digit bus ticket number by placing parentheses and symbols for arithmetic operations between some digits. The solution algorithm for a fixed number is reduced to enumerating all binary trees having exactly six terminal nodes with the signs of operations in internal nodes. For six-digit numbers that do not contain duplicate digits and the digit $0$, the problem has a solution for all numbers except the only number $746189$. It is impossible to obtain a hundred from this strange number $746189$.
Citation:
V. V. Borisenko, R. Rakhmatov, “A hundred from a bus ticket”, Fundam. Prikl. Mat., 23:3 (2020), 37–47; J. Math. Sci., 269:3 (2023), 290–297
Linking options:
https://www.mathnet.ru/eng/fpm1897 https://www.mathnet.ru/eng/fpm/v23/i3/p37
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