Random Math Quiz

I was doing the audit spreadsheet at work today, which has four numbers at the bottom of the sheet: the Guest Ledger, the City Ledger, the Advance Deposits, and the Total of all three.

As it happened, the decimal values on the Guest Ledger and City Ledger both happened to be the same- .58.  I at first was struck with a “what are the odds?” notion, but then I realized that, assuming all decimal values occur with the same regularity, the chance of the Guest Ledger and City Ledger matching would be 1 in 100, not really all that impressive.

But then I wondered- what would be the chance of all FOUR numbers matching?  What do you think?

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One thought on “Random Math Quiz

  1. Willow says:

    If you said 1 in 1,000,000, you’d be wrong. That would be the chance of four independent variables matching. However, the fourth number, the total of the other three, is a dependent variable, and in no way random.

    So we’re looking for the number of two-digit numbers (from 00 to 99) that fulfill the solution set 3X(mod 100)=X.

    If one first solves for the simpler 3x(mod 10)=X, with one digit numbers, one finds only two solutions- 0 (0 x 3= 0), and 5 (5 x 3= 15). As it happens, no two digit number ending in 5 ends in itself when multiplied by three, but 00 and 50 both do.

    So the first number- the Guest Ledger- has to end in .50 or .00, a 1/50 chance. The City Ledger and Advance Deposits each have a 1/100 chance of matching that, so we come out to a total chance of 1 in 500,000.

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