This puzzle was all about understanding numbers and logically working through the mathematicians's clues . The first step was really knowing place value, and most submitters had no trouble demonstrating their mastery of this concept.

Another key to solving this puzzle was understanding prime and composite numbers, as well as knowing how to classify 0 and 1. This proved a bit more difficult for some.

The three solutions below give a good sampling of the submissions to this puzzle. In each case, the submitter has explained how the clues were used to determine the digits of our mystery number. Notice how clues were combined to find some of the digits.

We encourage you to keep working on writing complete explanations of your work. When you use a math term, would it help to include a definition? If you didn't know one, where did you find it? What else might help if you were teaching this puzzle to a friend?

Solution prepared by a student from Norwalk, CT

My answer is 2614.

First, I figured out that the thousands place is a 2. I found this

out because the clue says "The smallest prime number is in the

thousands place." and two is the smallest prime number.

Second, I figured out that the hundreds place is a 6 because the clue

says "The digit in the hundreds place is three times the digit in the

thousands place." and 2x3=6

Next, I figured out that the tens place is a 1. I found this out

because the clue says "One of the digits is neither prime nor

composite." and a composite number is a number bigger than one

that has more than two factors. A prime number is a number that's only

factors are one and itself. This could also be 0, but if it was, then

there would be a 0 in the ones place also. Therefore, the answer is 1.

Finally, I figured out that the ones place is 4. I found this out

because the clue says "The digit in the ones place is four times the

digit in the tens place." The one has to be in the tens place to be

able to find out which number is in the ones place. Therefore, 1x4=4.

Therefore, the answer is 2614.

Solution Presented by a student from Owings Mills, MD

The answer to the first question is 2614 and that is

the license plate number.

First I figured out the fourth clue and the smallest

prime number is 2 so 2 is the answer to the fourth clue.

That means that 2 is in the thousands place.

Then I figured out the second clue and the answer to that

was 6 because 2 times 3 equals 6 so 6 is in the hundreds

place.

Then the answer to the first clue is 1 because 1 is neither

prime nor composite. The answer to the third clue is 4 because

the digit in the one's place is 4 times the digit in the

ten's place and 1 times 4 equals 4.  I knew even if 0 is

not prime nor composite, it still doesn't fit the answer

because in the first clue it says that one of its digits

is neither prime nor composite and in the third clue it

says that the digit in the one's place is four times the

digit in the ten's place and if you take 0 times 4 you

get 0 and there can only be one number that is neither

prime nor composite.

Then if you take all the numbers that were the answers

to the clues in order I get 2614 and 2614 is your answer!!!

Solution prepared by a student from  Bowman, SC

My final answer is two thousand six hundred fourteen.

  First we realized that the license's plate number was a four digit

number. It was a thousand's place, hundred's place, ten's place, and

one's place. Then we learned that one of the digits is neither prime

nor composite. The digit in the hundred's place is three times the

digit in the thousand's place. Also the digit in the one's place is

four times the digit in the ten's place. The smallest prime number

is in the thousand's place.

   Next we made a place value chart to figure out the answer to the

question. We made the thousand's place, hundred's place, ten's

place, and the one's place. After that we tried to put the clues

together, and get the right answer. We placed two in the thousand's

place. We got two because two is the smallest prime number. Next we

placed six in the hundred's place. We got six because it said

the digit in the hundred's place is three times the digit in the

thousand's place, so we multiplied two times three and got six. When

we got ready to find the digits for the tens and ones we knew it was

either two and eight or one and four because those were the only

digits that met the criteria for clue three. It wasn't two and eight

because it said that the digit in the thousand's place is the

smallest prime number. Therefore the two couldn't be in the ten's

place because the clue said the smallest prime number is in the

thousand's place. So we assume that no digit is used twice. For that

reason we could'nt use the two and eight. So thats why we placed the

one in the ten's place and the four in the one's place.

   Finally we came to an answer of two thousand three hundred

fourteen. We got it because we used the method of the place value

chart. Thousands  Hundreds   Tens   Ones

           2         6         1      4

        ________  ________   ____   ____

We also used the prime and composite method,and also the

multiplication method. That's how we found the license's plate

number on the back of the car.