!!!!! ***** CLUES - READ ONE AT A TIME IF YOU LIKE ***** !!!!!!
Clue 1. The quostient (answer) must be X 0 8 0 X (the 2 zeros are obvious since 2 Xs instead of one are brought down after subtraction) ask yourself how small can the last digit be?
ANSWER TO CLUE 1, AND NEW CLUE BELOW:
Answer to Clue 1: The last digit in the answer must be greater than 8 (hence = 9) since 8 times the divisor (XXX) yields a number of 3 digits, while the last digit yields a 4 digit number.
Clue 2. Ask yourself what do you know about the divisor (the "XXX") what's the bigest number it can be? (Note: this clue is independent from the first clue).
ANSWER TO CLUE 2, AND NEW CLUES BELOW:
Answer to Clue 2: The divisor must be less than 125, since from the "givens" we know that 8 times the divisor yields a 3 digit number, where as 8 times 125 or more yields a 4 digit number.
Clue 3. Can the first digit in the answer be as large as 9?
Clue 4. What else do you know about the first digit in the answer. If you multiply it by the divisor, and do the subtraction, how many digit are yielded? Based on that, what's the smallest number the first digit can be?
ANSWER TO CLUES 3 & 4, AND NEW CLUE BELOW:
Answer to Clue 3: The first digit in the answer cannot be 9 since we know that 9 times the divisor (XXX) yields a 4 digit number.
Answer to Clue 4: The first digit in the answer must be greater than 7, since 7 times a number less than 125 yields a number that would leave more than 2 digits after subtraction. Therefore, the first digit in the answer must be 8.
So, we know the answer (quotient) is: 8 0 8 0 9
Clue 5. Based on the quotient we now know, and the number of digits in the dividend (8), what's the smallest number the divisor can be?
FINAL ANSWER BELOW:
Answer to Clue 4: The divisor must be greater than 123, since 123 times 8 0 8 0 9 is a 7 digit number, whereas we are given that the dividend is an 8 digit number. So, the divisor is greater than 123, and less than 125 (see answer to clue 2), hence: it is 124!
