In the main draw of a lottery, six of the balls (which are numbered from 1 to 49) are selected at
random, then the numbers chosen are rearranged and displayed in ascending numerical order.
For instance: 3 17 20 29 34 45
In one draw recently, I noticed that the six numbers were made up of a total of ten digits, all
different. The lowest number on this occasion was 1 and the highest number was 49, so the
range of the six numbers was 48, the greatest possible range for the lottery main draw.
What is the smallest possible range when the six numbers in the main draw of the lottery have
a total of ten digits, all different?
I don't get this at all.
8 , 9 , 17 , 26 , 35 , 40
How did you work this out
Did you get in?
To find the smallest possible range when the six numbers in the main draw of the lottery have a total of ten digits, all different, we can start by considering the minimum and maximum possible values for the six numbers.
Since all the numbers must be different, the first number in the draw must be 1. This is because any number higher than 1 would increase the range.
Next, we need to find the highest 5-digit number that we can include while still keeping the total number of digits at 10. The highest possible 5-digit number is 9,876, which has 5 unique digits. So, we can include 9,876 as the second number.
For the third number, we need to find the highest 4-digit number with unique digits. This would be 6,543.
For the fourth number, we can pick the maximum 3-digit number with unique digits, which is 2,198.
For the fifth number, we can choose the highest 2-digit number with unique digits, which is 87.
Finally, for the sixth number, we can pick the remaining single-digit number, which would be 5.
To find the range, we subtract the lowest number (1) from the highest number (9,876):
Range = 9,876 - 1 = 9,875
Therefore, the smallest possible range when the six numbers in the main draw of the lottery have a total of ten digits, all different, is 9,875.
Well, let me try to explain it to you in a humorous way!
Imagine the lottery balls are bunch of mischievous clowns, each one with a unique number painted on their colorful outfits. Now, the lottery organizers randomly select six of these clown balls.
In this particular draw, these clowns couldn't resist showing off their digits, which means that the six numbers chosen had a total of ten different digits. It's like they were saying, "Look at us, we're unique and special!"
But, just like any gathering of clowns, there has to be an order, right? So, the numbers are rearranged in ascending numerical order. It's like lining up the clowns from the shortest to the tallest.
Now, in this circus of numbers, the lowest clown was number 1, and the tallest clown was number 49. So, the difference between these two extreme clowns gives us the range, which in this case is 48. It's the largest possible range for the lottery main draw.
But what about the smallest possible range? That's the tricky part! We want the range to be as small as possible while still having all ten digits covered.
So, let's imagine a scenario where the clowns were feeling a bit more organized. This time, they decided to line up in a row in such a way that the difference between the tallest and the shortest clown is the smallest possible.
In this case, they would line up like something crazy, I'm talking about numbers like 1, 2, 3, 4, 5, and 10. The range here would be just 9, because the tallest clown's number is 10 and the shortest clown's number is 1.
So, in conclusion, the smallest possible range when the six numbers in the main draw of the lottery have a total of ten digits, all different, is 9. It's like the clowns had a small but well-organized party!
Hope that gives you a clearer picture, or should I say, a fun circus act!