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 Write-up

Title
Collecting Stamps

Problem Statement
Jessica has an odd number of stamps in her collection. The sum of the digits in the number of stamps she has is 12. The hundreds digit is three times the ones digit. If she has between 1000 and 2000 stamps in her collection, how many stamps does Jessica have?

Problem setup

Figure out how many stamps Jessica has based on the clues given.  The answer must be between 1000-2000 and must be an odd number.  The sum of the digits must = 12.  The hundreds digit = 3 times the ones digit.

Plans to Solve/Investigate the Problem

The thousands digit must be 1.  Use guess and check to determine the other digits.

Investigation/Exploration of the Problem

The ones digit must be 1, 3, 5, 7, or 9 in order for the number to be an odd number.  It can't be 9, 7, 5, or 3 since the hundreds digit would have to be 27, 21, 15, or 9.  27, 21, & 15 are impossible since they are not single digits.  If the ones digit was 3, the hundreds digit would be 9.  Then the digits 1 (thousands place), 9 (hundreds place), and 3 (ones place) would equal more than 12.  So the ones digit must be 1.  That would mean the hundreds place would be 3.  1 (thousands place), 3 (hundreds place), and 1(ones place) equal 5 so the tens digit must be 7.  That would mean the number of stamps is 1371.  This is an odd number between 1000 and 2000.  The sum of its digits equals 12.  The hundreds digit, 3, is three times the ones digit, 1.

1 + 3 + 7 + 1 = 12.  3 x 1 = 3

Jessica has 1,371 stamps.

Extensions of the Problem

Investigate to discover the closest solution that would not use any digits more than once.  One possible solution to this might be 1,953.  This odd number is still between 1,000 and 2,000, and the hundreds digit is still three times the ones digit.  The exception is that the digits equal 18.

Look to see if there is any correlation between the number of stamps being an odd number yet the sum of its digits is an even number.  The above solution is still an example of an odd number with its sums equaling an even number.  If the solution was 1,632, the digits equal 12 - an even number with its sum equaling an even number.  But the hundreds digit is still 3 times the ones digit.  What other solutions along this line could you find?

Author & Contact
Vicki Hughes
vhughes@rockdale.k12.ga.us

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