Difference between revisions of "G285 2021 MC-IME I"
Geometry285 (talk | contribs) (Created page with "==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>4</math> digits of <cma...") |
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[[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 ![\[\sum_{i=1}^{100} a_i\]](http://latex.artofproblemsolving.com/d/a/6/da699257a73b90382a078d2633d62f8bcf06f67d.png)
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 
.
