One digit in each of these identification numbers of a postal money order is smudged. Can you recover the smudged digit, indicated by a Q, in each of these numbers? a) 493212Q0688 b) 850Q9103858 c) 2Q941007734 d) 66687Q03201

a) Q = 0 or 9

b) Q = 5

c) Q = 7

d) Q = 8

Step-by-step explanation:

We assume the postal money order to be of the United State. A smudged digit is calculated using the following algorithm.

1. Add first 10 digits of 11-digit number.

2. Divide the sum of the 10 numbers by 9.

3.The remainder is the smudged digit.

4.The smudged digit is appended to the end of the ID number or anywhere in the number.

It is calculated as:

a) 493212Q0688

Therefore, Q is either 0 or 9.

b) 850Q9103858

Therefore, Q is 5 because from Q mod 9 = 5, we have Q = 5 mod 9.

c) 2Q941007734

Therefore, Q is 7 because we have to cancel out the negative sign by adding the modulo base (9) to the negative number: -2 + 9 = 7.

d) 66687Q03201

Therefore, Q is 8 because we have to cancel out the negative sign by adding the modulo base (9) to the negative number: -1 + 9 = 8.

529 and 531

step-by-step explanation:

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.