Geodesic
A~hundred from a~bus ticket
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 37-47.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $746189$. 
@article{FPM_2020_23_3_a3,
     author = {V. V. Borisenko and R. Rakhmatov},
     title = {A~hundred from a~bus ticket},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {37--47},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a3/}
}
TY  - JOUR
AU  - V. V. Borisenko
AU  - R. Rakhmatov
TI  - A~hundred from a~bus ticket
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2020
SP  - 37
EP  - 47
VL  - 23
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a3/
LA  - ru
ID  - FPM_2020_23_3_a3
ER  - 
%0 Journal Article
%A V. V. Borisenko
%A R. Rakhmatov
%T A~hundred from a~bus ticket
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2020
%P 37-47
%V 23
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a3/
%G ru
%F FPM_2020_23_3_a3
V. V. Borisenko; R. Rakhmatov. A~hundred from a~bus ticket. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 37-47. http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a3/

[1] Lando S. K., Lektsii o proizvodyaschikh funktsiyakh, MTsNMO, M., 2007

[2] Shen A., Programmirovanie. Teoremy i zadachi, MTsNMO, M., 2007

[3] Davis T., Catalan Numbers, 2006 http://www.geometer.org/mathcircles

[4] Črepinšek M., Mernik L., “An efficient representation for solving Catalan number related problems”, Int. J. Pure Appl. Math., 56:4 (2009), 589–604 | MR