Problema Solution
The digits 0, 1, 2, 4 are used exactly once to make a series of integers greater than 1000. Find the difference between the median of all the integers that can be created and the average of the largest and smallest integer that can be created.
Answer provided by our tutors
the numbers that can be made from the digits 0, 1, 2, 4 used exactly once and are greater than 1000 are
1024, 1204, 1240, 1042, 1402, 1420
2014, 2104, 2140, 2041, 2401, 2410
4012, 4102, 4120, 4021, 4201, 4210
To find the Median, place the numbers in value order and find the middle pair of numbers, and then find the value that would be half way between them:
1024, 1042, 1204, 1240, 1402, 1420, 2014, 2041, 2104, 2140, 2401, 2410, 4012, 4021, 4102, 4120, 4201, 4210
the middle pair is 2104 2140 thus the median is: (2104 + 2140)/2 = 2122
the average of the largest and smallest integer is: (1024 + 4210)/2 = 2617
the difference between the median of all the integers that can be created and the average of the largest and smallest integer is:
2122 - 2617 = - 495.