Difference between revisions of "1997 PMWC Problems/Problem I2"
(New page: ==Problem== In the multiplication in the image, each letter and each box represent a single digit. Different letters represent different digits but a box can represent any digit. What does...) |
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Revision as of 12:36, 10 January 2009
Problem
In the multiplication in the image, each letter and each box represent a single digit. Different letters represent different digits but a box can represent any digit. What does the five-digit number HAPPY stand for?
Solution
Following the rules of multiplication, we see that 9 times the units digit of the three digit number ends in 7, which means that the digit must be a 3. Carrying out the multiplication, we see that the last two digits of the second product are 17, which means that the hundreds digit in the first product must be a 4. We now have
-13 *9- ___ -49- --17 _____ HA66Y
The only digit that would work as the units digit of 9- is 7. Therefore we have
-13 *97 ___ -491 --17 _____ HA661
The only multiple of 7 that is two digits and is 7 times a digit is 14. Therefore we have
213 *97 ___ 1491 1917 _____ 20661
