MathDB

15

Part of 2019 BMT Spring

Problems(2)

2019 BMT Team 15

Source:

1/7/2022
A group of aliens from Gliese 667667 Cc come to Earth to test the hypothesis that mathematics is indeed a universal language. To do this, they give you the following information about their mathematical system:
∙\bullet For the purposes of this experiment, the Gliesians have decided to write their equations in the same syntactic format as in Western math. For example, in Western math, the expression “5+45+4” is interpreted as running the “++” operation on numbers 55 and 44. Similarly, in Gliesian math, the expression αγβ\alpha \gamma \beta is interpreted as running the “γ\gamma ” operation on numbers α\alpha and β \beta.
∙\bullet You know that γ\gamma and η\eta are the symbols for addition and multiplication (which works the same in Gliesian math as in Western math), but you don’t know which is which. By some bizarre coincidence, the symbol for equality is the same in Gliesian math as it is in Western math; equality is denoted with an “==” symbol between the two equal values.
∙\bullet Two symbols that look exactly the same have the same meaning. Two symbols that are different have different meanings and, therefore, are not equal.
They then provide you with the following equations, written in Gliesian, which are known to be true: https://cdn.artofproblemsolving.com/attachments/b/e/e2e44c257830ce8eee7c05535046c17ae3b7e6.png
combinatorics
2019 BMT Individual 15

Source:

1/9/2022
How many distinct positive integers can be formed by choosing their digits from the string 0407201904072019?
combinatorics