# This one might be tricky

• Feb 27th 2008, 01:55 AM
goodz
This one might be tricky
This is for a game I play,

you can take a "som" of a person, it gives you a number, but the number is not 100% accurate it can be off by +/- 45%, there is no way to tell how far off it is with just 1 number.

You can take multiple "soms" to get 2, 3 or 4 numbers all off by different percents from the correct number.

the numbers can be off by 1% 4% 18% etc. but can not be off by something like 1.34% or 6.542%. They are off by whole percents.

The maximum error is 45%

Using this I think it should be possible to make a formula to figure out the correct answer given 3-4 numbers.

I wanted to work this into a spread sheet but I got a little stuck... :)

whoops this probably is in the wrong section, I am definitely in first year university
• Feb 27th 2008, 06:58 AM
colby2152
Can you shed some light on the actual writing of the question? It seems a bit ambiguous to me.
• Mar 4th 2008, 02:31 AM
goodz
managed to get a spreadsheet up that does it, had to use arrays so had to get a bit of help on the programming end of things,

it ended up not being a math question at all really.

i think it would be something like

f(x)= x*b
f(x)= x*a

(a is a integer between +/- 1-45)
(b is a int between +/- 1-45)

solve for x, in some cases u needed a c, or even rarely a d. if b and a were equal ofc u get infinite results.

it was for a game where you arent supposed to figure out the exact number, so there is some uncertainty but using this spread sheet :D
• Mar 6th 2008, 03:58 PM
iknowone
Let $n$ be the unknown number. Say the first trial gives the value $k$. Then we can conclude that $n$ is between $\frac{k}{1.45} \text{ and } \frac{k}{.45}$

trial 2 gives a result of $j$. Again:
$n$ is between $\frac{j}{1.45} \text{ and } \frac{j}{.45}$. since we have information from the previous round about the interval in which $n$ could be, intersect the two intervals.

repeat.

But will this always terminate with a conclusion " $n$ must be..."??
No, since the number k could come up every single round and no new information is gained. If we require that a new number be given every single round then the worst case scenario is around $\frac{n}{.45}-\frac{n}{1.45}$ rounds, since every integer in the interval $[.45n,1.45n]$ might come up.

An interesting question is, what is the expected number of steps required for you to be 10% or 50% or 95% sure of the number?