Post by jsonchiu on Aug 2, 2009 16:43:24 GMT -8
The Great Battle of Ants - 5 math questions.
Synopsis: there are lots of ants in my house and the ants are quite annoying. For simplicity sake, let's say there are 10000 ants. Here, I'm tired of them, so I want to improve my quality of living by reducing ants to less than 100 for at least 1 day.
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Level 1
I have invented an ant-machine. The machine kills half of the ants every 3 days at 7am. How many days does it take to reach my goal (<100 ants)?
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Level 2
After #1, A few months later, the ants grow back to the original size (10000) because of my neglect. This time, they have imported a new species of ants to help them breed off springs at a faster rate as to counter the ant machine. The ants will double every 5 days at 12pm.
So now, every 3 days, ant-machine kills half of the ants, every 5 days, ants double. How many days does it take to get to my goal (<100 ants)?
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Level 3
The ants, after finding limits to their breeding speed, began to seek help from other pests. The rats and cockroaches agree to help them destroy the ant-machine with the promise of more food brought by ants. Every 7 days, the machine power halves at 3pm. (e.g. when full power, 10000 --> 5000, when half power, 10000 --> 7500, when 1 quarter power, 10000 --> 8750)
So now, every 3 days ant-machine kills ants, every 5 days, ants double, every 7 days machine power halves. How many days does it take to get to my goal (<100 ants)?
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Level 4
After a blooming growth of pest population, I found out about the ant machine being broken. Thus I begin to repair the ant-machine to FULL power every 10 days at 7pm.
So now, every 3 days ant-machine kills ants, every 5 days, ants double, every 7 days machine power halves, every 10 days machine power -> full. How many days does it take to get to my goal (<100 ants)?
---------------------------
Level 5
The "Ant God" sees the living spirits of the ants. Thus, to help them, every perfect number day (perfect numbers - a number that is equal to the sum of its factors, e.g. 6=1+2+3, 28 = 1+2+4+7+14, 496, 8128, etc), he will revive 10000 ants at 11:59pm
So now, every 3 days ant-machine kills ants, every 5 days, ants double, every 7 days machine power halves, every 10 days machine power -> full, every perfect-number-day ants + 10000. How many days does it take to get to my goal (<100 ants)?
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Go ahead! solve!
Synopsis: there are lots of ants in my house and the ants are quite annoying. For simplicity sake, let's say there are 10000 ants. Here, I'm tired of them, so I want to improve my quality of living by reducing ants to less than 100 for at least 1 day.
-------------------------
Level 1
I have invented an ant-machine. The machine kills half of the ants every 3 days at 7am. How many days does it take to reach my goal (<100 ants)?
-------------------------
Level 2
After #1, A few months later, the ants grow back to the original size (10000) because of my neglect. This time, they have imported a new species of ants to help them breed off springs at a faster rate as to counter the ant machine. The ants will double every 5 days at 12pm.
So now, every 3 days, ant-machine kills half of the ants, every 5 days, ants double. How many days does it take to get to my goal (<100 ants)?
-----------------------
Level 3
The ants, after finding limits to their breeding speed, began to seek help from other pests. The rats and cockroaches agree to help them destroy the ant-machine with the promise of more food brought by ants. Every 7 days, the machine power halves at 3pm. (e.g. when full power, 10000 --> 5000, when half power, 10000 --> 7500, when 1 quarter power, 10000 --> 8750)
So now, every 3 days ant-machine kills ants, every 5 days, ants double, every 7 days machine power halves. How many days does it take to get to my goal (<100 ants)?
---------------------------
Level 4
After a blooming growth of pest population, I found out about the ant machine being broken. Thus I begin to repair the ant-machine to FULL power every 10 days at 7pm.
So now, every 3 days ant-machine kills ants, every 5 days, ants double, every 7 days machine power halves, every 10 days machine power -> full. How many days does it take to get to my goal (<100 ants)?
---------------------------
Level 5
The "Ant God" sees the living spirits of the ants. Thus, to help them, every perfect number day (perfect numbers - a number that is equal to the sum of its factors, e.g. 6=1+2+3, 28 = 1+2+4+7+14, 496, 8128, etc), he will revive 10000 ants at 11:59pm
So now, every 3 days ant-machine kills ants, every 5 days, ants double, every 7 days machine power halves, every 10 days machine power -> full, every perfect-number-day ants + 10000. How many days does it take to get to my goal (<100 ants)?
--------------------------
Go ahead! solve!