Difference between revisions of "G285 2021 MC-IME I"
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==Problem 1== | ==Problem 1== | ||
| − | Let a recursive sequence <math>a_n</math> be defined such that <math>a_1=20</math>, and <math>a_n=16a_{n-1}+4</math>. Find the last <math> | + | Let a recursive sequence <math>a_n</math> be defined such that <math>a_1=20</math>, and <math>a_n=16a_{n-1}+4</math>. Find the last <math>3</math> digits of <math>a_{100}</math> |
[[G285 2021 MC-IME I Problem 1|Solution]] | [[G285 2021 MC-IME I Problem 1|Solution]] | ||
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| + | ==Problem 2== | ||
| + | If the number <math>abcd_{11}</math> is a palindrome in base <math>7</math>, and <math>dcba</math> expressed in base <math>10</math> does not begin with a nonzero digit, find the difference between the largest and smallest possible sum of <math>a+b+c+d</math>. | ||
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| + | [[G285 2021 MC-IME I Problem 2|Solution]] | ||
be defined such that 
, and 
. Find the last 
digits of 
is a palindrome in base 
, and 
expressed in base 
does not begin with a nonzero digit, find the difference between the largest and smallest possible sum of 
.
