Question 623888
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Let *[tex \LARGE a] represent the 1000s digit, *[tex \LARGE b] represent the 100s digit, *[tex \LARGE c] represent the 10s digit, and *[tex \LARGE d] represent the 1s digit.


Constraints, each digit in the range *[tex \LARGE 0\ \leq\ x\ \leq\ 9]


From the first given relationship:  *[tex \LARGE a\ =\ b\ +\ 5]


So we know that *[tex \LARGE b\ \leq\ 4] otherwise *[tex \LARGE a\ >\ 9]


From the second relationship:  *[tex \LARGE d\ =\ a\ +\ b], but by substitution we can write *[tex \LARGE d\ =\ 2b\ +\ 5].  This further restricts *[tex \LARGE b\ \leq\ 2] so that *[tex \LARGE d\ \not{>}\ 9]


From the third relationship:  *[tex \LARGE c\ =\ a\ -\ b\ =\ b\ +\ 5\ -\ b\ =\ 5]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ b\ =\ 2\ \Rightarrow\ a\ =\ 7\ \wedge\ d\ =\ 9]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ b\ =\ 1\ \Rightarrow\ a\ =\ 6\ \wedge\ d\ =\ 7]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ b\ =\ 0\ \Rightarrow\ a\ =\ 5\ \wedge\ d\ =\ 5]


So the number is 7259 or 6157 or 5055


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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