Difference between revisions of "2022 SSMO Speed Round Problems/Problem 6"
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| + | ==Problem== | ||
| + | At the beginning of day <math>1</math>, there is a single bacterium in a petri dish. During each day, each bacterium in the petri dish divides into <math>a>1</math> new bacteria, and <math>b\ge 1</math> bacteria are added to the petri dish (these bacteria do not divide on the day they were added). For example, at the end of day <math>1</math>, there are <math>a+b</math> bacteria in the petri dish. If, at the end of day <math>4</math>, the number of bacteria in the petri dish is a multiple of <math>48</math>, find the minimum possible value of <math>a+b</math>. | ||
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| + | ==Solution== | ||
Latest revision as of 19:14, 2 May 2025
Problem
At the beginning of day 
, there is a single bacterium in a petri dish. During each day, each bacterium in the petri dish divides into 
new bacteria, and 
bacteria are added to the petri dish (these bacteria do not divide on the day they were added). For example, at the end of day , there are 
bacteria in the petri dish. If, at the end of day 
, the number of bacteria in the petri dish is a multiple of 
, find the minimum possible value of .
