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JOURNALS // Fundamentalnaya i Prikladnaya Matematika // Archive

Fundam. Prikl. Mat., 2020 Volume 23, Issue 3, Pages 37–47 (Mi fpm1897)

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 $746189$.

UDC: 004.02


 English version:
Journal of Mathematical Sciences (New York), 2023, 269:3, 290–297


© Steklov Math. Inst. of RAS, 2025