Assuming that you want to discount luck (if not, the answer would be 1), and that the guesser always guesses the median of the remaining range, the answer would be the (ceiling of the log(base 2) of the count of numbers in the range). If the log(base 2) is an exact integer, add 1.
Example 1, pick a number between 1 and 9. There are 9 numbers in the range, so the log(base2) of 9 is ~3.16. The ceiling of that is 4. Do not add 1 for a final answer of 4.
The full range is 1,2,3,4,5,6,7,8,9. The median is 5
First guess is 5. Higher - 6,7,8,9 is remaining range. 7 and 8 are the median numbers
Second Guess is 8. Lower - 6,7 is the remaining range. 6 and 7 are the median numbers.
Third guess is 7. Lower - 6 is the remaining range. 6 is the median number
Fourth guess is 6. Correct.
Example 2, pick a number between 1 and 16. There are 16 numbers in the range, so the log(base 2) of 16 is 4. The ceiling of 4 is 4. Add the 1 because the Log(base 2) is an integer, for a final answer of 5.
Full range is 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16. The median numbers are 8 and 9.
First Guess is 9. Lower - 1,2,3,4,5,6,7,8 is the remaining range. 4 and 5 are the median numbers
Second Guess is 4. Higher - 5,6,7,8 is the remaining range. 6 and 7 are the median numbers.
Third Guess is 6. Higher - 7,8 is the remaining range. 7 and 8 are the median numbers.
Fourth Guess is 7. Higher - 8 is the remaining range. 8 is the median.
Fifth guess is 8. Correct
Both of these examples show worst case scenarios. A "lucky guess" will reduce the number of guess needed, possibly all the way to 1.
Note: I do realize that to a math purist, in the examples where I said that the median numbers were x and y, the correct answer is that the median number is between x and y. Since I can not guess the number between the two numbers, I am bending the definition of median to treat the two bordering numbers as the median when the strict definition would list the median as being between those two numbers.
3
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7 mm
A minimum of 6 sets of data are needed to make a valid conclusion.
3
Minimum GPA at USC is a 3.0
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The minimum number of seismographs needed to locate an epicenter of an earthquake is 3.
Isn't any minimum or maximum.
the standard of living
they have to be a minimum height of between 5'4" and 5'5"
Minimum 45% is required to get the admission
minimum needed is $10,000.00
19%
The minimum number of seismic stations needed to determine the location of an earthquake's epicenter is THREE.
The amount of heat needed to raise an object's temperature depends on its mass, its specific heat capacity, and the temperature change desired. Objects with higher mass require more heat to raise their temperature, while those with higher specific heat capacities absorb more heat for the same temperature change.
24,000