Two non-zero digits x and y were randomly (uniform distribution) generated by a computer.
I. What is the probability that x-y is a multiple of 4 ?
Ii. Same question for 5 instead of 4.
This is how I solved it in my head.
Picture a 9x9 grid (1-9 in both directions). One long diagonal is where the numbers are equal x-y=0. There are 9 in this diagonal.
In the next diagonal there are 8 numbers of difference 1.
In the next diagonal there are 7 numbers of difference 2.
In the next diagonal there are 6 numbers of difference 3.
In the next diagonal there are 5 numbers of difference 4. <---
In the next diagonal there are 4 numbers of difference 5.
In the next diagonal there are 3 numbers of difference 6.
In the next diagonal there are 2 numbers of difference 7.
In the next diagonal there is 1 numbers of difference 8. <----
There's another set of diagonals on the other side with negative differences.
Total for part I: 9+5+5+1+1=21 Probability 21/81=7/27
Total for part Ii: 9+4+4 Probability 17/21
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Posted by Jer
on 2022-03-28 10:38:20 |
In my head solution
