Suggested Fraud Test
Mon, 2024-11-04 11:53
#1
Suggested Fraud Test
How many numbers of one up to 10.N^2 i.e 10.(N squared) begin with the digit 1, i.e. a One?
To confirm, for N=5, I have here 105, for N=10 there are 460, and for N=20 there are 1920 numbers beginning with the digit 1
You could test the answers with a small computer program, a good exercise too! The idea might be used in testing consistency and for detection of fraud.
Incorrect
The numbers are incorrect they should be much larger, I will have to look at it again. Perhaps someone could be before me!
In principle I think the idea will work and is in order.
Sorry about that! Tom
Solution
I have now discovered the solution is a great deal simpler than I thought! Some people talk of "clock arithmetic". If N is the given number we must solve Nmod 9 = 1 , it is N = 9Q + R with R=1 where is Q the quotient and R the remainder of N divided by 9.
Q is the number asked, how many numbers start with the digit 1 and is less than N.
Later on I will put the story on Abc with more explanation and my ideas for consistency testing in lists of numbers.
Complicated Man, Yes for instance a statement like "This sentence is false." Or “ I am not.", does sound rather odd doesn't it? What about “Zero multiplied by Infinity”? Or, “what is One divided by Zero?” The Archimedes buoyancy principle was your perfect example of such confusion.
Used to hate that sign. Sorry I don't have a light Smokin Man smoking is bad for your health, and your wallet, and bad example for the kids.
Answers and Remarks
My answers are now on the ABC story, Consistency in Lists of Numbers
https://www.abctales.com/story/tom-brown/consistency-lists-numbers
There were inaccuracies I think they have been sorted out now.
Keep well! And all the best! Tom