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.