Geodesic
A hundred from a bus ticket
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 37-47
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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 $746189$. 
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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