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**doobster****Member**- Registered: 2005-12-07
- Posts: 3

I'm trying to play a game in which you need to guess a random number between 1 and 10 million!

These are the messages you receive after guessing:

higher and lower by 100,002 - freezing

You are between 30,002 and 300,000 points, higher or lower - cold

You are between 10,002 and 100,000 points, higher or lower - warm

when you get within 10,000 you only get a note saying you are red hot - hot

I was hoping someone could help me develop a process to guess the number in the least amount of guesses.

Thanks.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,619

You don't get any "too high" or "too low" message?

If they don't tell you that, then you would want to search for the boundary between two regions.

But your boundaries don't make sense ... what if you are within 50,000, does it say "warm" or "cold" ?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**doobster****Member**- Registered: 2005-12-07
- Posts: 3

Hi there, I posted the messages i receive.

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**Wanna be math wiz****Member**- Registered: 2005-11-24
- Posts: 38

I dont fully understand the game but i will give a guess of 6 million.

Imagination is more important than knowledge

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,619

But doobster, you haven't answered my question.

So I can't develop a strategy for you unless I can understand how the system works.

If you are within 50,000, does it say "warm" or "cold" ?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**doobster****Member**- Registered: 2005-12-07
- Posts: 3

i don't know if i fully understand them either, but i think:

anything above 100,000 will receive freezing.

> 30,000 and < 100,000 will receive cold

> 10,000 and < 30,000 will receive warm

< 10,000 hot

this is just an assumption, but i think it makes a little bit of sense lol

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,619

OK, so the problem is that you could receive a "hot" but still have 20,000 numbers to check.

But if you knew that, say 250,200 was "warm", but 250,201 was "hot" you would then know that 250,201+10,000=260,201 was the number.

So, use "binary search" to find where one zone becomes another, and then jump from there to the center.

"Binary search" just means halving your guesses each time.

An example: Say the boundary between "warm" and "hot" is 71/72, and let us limit our search to 1 (which is warm) to 100 (which is hot).

First Guess (half way between 1 and 100): 50 warm

Next Guess (half way between 50 and 100): 75 hot

Next Guess (half way between 50 and 75): 63 warm

Next Guess (half way between 63 and 75): 69 warm

Next Guess (half way between 69 and 75): 72 hot

Next Guess (half way between 69 and 72): 71 warm DONE!

We now know that 71 is warm and 72 is hot. And we could (theoretically) jump forward 10,000 to the answer.

Get it?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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