Senior Prom - posted May 19, 2003

The Senior Prom is coming up, and three couples are going out to dinner and then on to the dance together. From the clues below, can you determine which girl (Diana, Sophia or Tameka) is going to the prom with which boy (Anthony, Derrick or Javiar), and what color dress (lilac, rose or white) each girl is wearing?

• Derrick's date is not Tameka.
• Anthony's date is not wearing a white dress.
• Javiar's date is wearing a rose dress.
• Tameka is not wearing a lilac dress.
• Sophia is wearing a white dress.

Be sure to clearly explain the thinking that you used to find your answer.

Comments

This problem was a nice way to finish the year. There were 59 solutions submitted, and every one of you correctly solved the problem and figured out who went to the prom with who and what color dress each girl was wearing. Great job!

There were a lot of comments from people saying that they really like this kind of problem because it requires thought and logic rather than lots of calculations. Several of you said that the ability to think clearly and logically is the sort of thing that you will use in the 'real world'.

Some of you did not earn credit because you did not explain the thinking you used to find your answer. Remember that a clear and complete explanation of your work is just as important as having the right answer, and in the problem it says, 'Be sure to clearly explain the thinking that you used to find your answer.' Saying things like 'I used logical thinking' or 'I made a chart and filled it in using the clues' doesn't help the reader understand the thinking you did to reach your conclusions.

Let's look at some examples of good clear explanations. Making a table is the 'classic' way to do a logic problem like this, and many of you used that approach. Mark Cerqueira used html in his solution to make really nice tables and did a great job of showing and explaining each step of filling in the table. Kelly Porter showed two finished tables and clearly explained the logic she used to fill them in.

Nothing in the problem says that you have to use the clues in the order they are presented. A lot of you started with the ones towards the end, using them to first figure out what color dress each girl was wearing, and then matching up the boys. I think that was the easiest way to do the problem. Check out the solutions of the team of Edison Brito and Jose Santiago and the team of Jonathan Munoz and Erick Delgado for good examples of matching the girls and dresses first.

Janeli Melendez and Kristen Afonso each started by matching the boys to the colors and then deciding which girl went with which.

Others worked towards matching it all up at once rather than doing all the colors and then all the girls or boys. Take a look at the solutions of Ned Wogwugwu, Richard Smith and Hector Melendez. Ned also did a very nice job of checking his solution, earning marks for Reflection.

These highlighted solutions, and all the ones shown in the 'More Solutions' link, did a nice job of explaining the thinking that led to the answer.

I had fun reading your solutions on this problem. It was very interesting to see how many different ways people thought about the five given clues to come up with the right combination of couples and colors. I encourage you to take a look at more of the solutions by following the link at the bottom of the page.

Congratulations to everyone who earned credit on this problem, and have a great summer!

- Riz

Highlighted solutions:

Sophia is going with Derrick in a white dress;Diana is going with
Anthony in a lilac dress; and Javier is going with Tameka in a rose
dress.

  The problem says that three couples are going to the senior prom.
With the clues given we are to find out who's going to the prom with
who.
  The first clue says that Derrick's date is not Tameka.  From this
clue you coould narrow it down that Derricks date could be either
Sophia or Diana.
  The second clue says that Anthony's date is not wearing a white
dress which narrows it down to his date either having a lilac dress
or a rose colored dress.
  The third clue says rgar Javier's date is wearing a rose dress.  So
this means that Anothony's date is weaing a lilac dress she is not
wearing white like it was stated in the second clue and neither
wearing rose because Javier's date is wearing rose.  Derrick's date
is now left wearing the white dress.
  The fourth clue says that Tameka is not wearing a lilac dress,
which means her date can not be Anothony.  So she is narrowed down to
being Derrick's or Javier's date.
  The last clue says that Sophia is wearing a white dress which means
she is Derrick's date.  Since she is Derrick's date then Tameka is
Javier's date because she is not wearing lilac.  Leaving Diana as
Anthony's date.
  So basically it goes like this:
                 Derrick-->Sophia--> white
                 Anthony--> Diana--> lilac
                 Javier--> Tameka--> rose

Javiar is Tameka's date. Anthony is Diana's date, and Derrick is
Sophia's date. Diana was wearing a lilac dress. Sophia was wearing a
white dress, and Tameka was wearing a rose dress.

    Well, in order to work this problem, we went through the steps
backwards. For instance we worked from the last clues, up to the top.
So therefore, the first clue we recorded was that: Sophia is wearing
a white dress.
      Now we have the color of one of the girl's dresses. So, we can
see that either Tameka or Diana is wearing a pink or lilac dress,
which leads us to our second clue that says:Tameka is not wearing a
lilac dress. Then that means, Tameka is wearing a rose dress. Now we
have all the colors that the girls were wearing.

                    Sopia was wearing white.
                    Tameka was wearing rose.
(By doing the process of elimination): Diana was wearing lilac.

   Now we have to figure out their dates. The next clue says:
Javiar's date is wearing a rose dress. Instantly, we already know
that Javiar's date is Tameka.
    The next clue says:Anthony's date is not wearing a white dress.
We know his date isnt Sophia and we know it isnt Tameka either
because she's going with Javiar. This leaves us with Diana who was
wearing lilac. Now we have two couples:

                          Javiar and Tameka
                                 and
                          Diana and Anthony

Since Derricks date is not Tameka since shes already going with
Javiar, this leaves us with Derrick and Sophia!

Now we have completed the problem which looks like this:

Couples                       Colors of the dresses

Javiar & Tameka               Tameka- rose

Diana and Anthony             Diana- lilac

Derrick and Sophia            Sophia- white

the dates for the prom will be Derrick with Sophie which is wearing a
white dress, Anthony and Diana with a liliac colored dress, and
Javiar and Tameka with a rose colored dress.

I am told that Derrick's date is not Tameka, so that leaves Diana
and Sophia. I am then told that Anthony's date is not wearing white
so that leaves his date with a rose or liliac dress. Next I am told
that Javiar's date is wearing a rose dress, so that tells me
Anthony's date is wearing liliac and Derrick's date is wearing white.
I am then told that Tameka is not wearing liliac so she is not
Anthony's date. I am also told that Sophia is wearing white so she is
Derrick's date. Since Tameka is not wearing liliac and Sophia is
wearing white this tells me that Tameka is wearing a rose colored
dress making her Javiar's date. I am then left with the final couple
Anthony, Diana, and a liliac dress.
This then gives me the couples Derrick and Sophia in a white dress,
Anthony and Diana in a liliac dress, and Javiar and Tameka in a rose
dress.

The prom dates are:Tameka is going with Javier while wearing the
rose dress, Sophia is going with Derrick while wearing the white
dress, and Diana is going with Anthony while wearing the lilac dress.

We first started by stating the facts. We already know that Sophia
is wearing the white dress. Tameka is not wearing the lilac dress
but niether the white dress because Sophia is wearing the white
dress; so she is wearing the rose dress.That means that Diana is
wearing the lilac dress because that is the last one left.

So, so far we know that:
                         Diana is wearing the lilac dress.
                         Sophia is wearing the white dress.
                         Tameka is wearing the rose dress.

From the data above we know Javier's date is wearing the rose which
is Tameka. Anthony's date is not wearing a white dress so it can't
be Sophia so it is Diana because Tameka is taken. Last Sophia goes
with Derrick because they are the only two left.

Derrek-n-Sophia, Javier-n-Tameka, and Anthony-n-Diana.

If Sophia is wearing White and Anthony is not and Javier is wearing
Rose than Derreck is Sophia's date.

If Anthony is not wearing White and Javier is wearing Rose, than
Anthony would have to be wearing Lilae.

If Tameka is not wearing Lilae but Sophia is wearing White, that
means Anthhony is Diana's date.
                               1.Javier-Tameka(Rose)
                               2.Derrek-Sophia(White)
                               3.Anthony-Diana(Lilae)

After going throught the information thoroughly, i have come to a
conclusion that Javier is going to prom with Tameka who is wearing a
rose dress, Derrick is going with Sophia who is wearing a white
dress, and Anthony is going with Diana who is wearing a lilac dress.

First i went through the given information and familiarized myself
with the problem. Next I pinpointed which girl was wearing what
dress.
Tameca was not wearing a lilac dress, and Sophia was wearing a white
dress, that means Tameka's dress is rose..... Javier's date Tameka is
wearing a rose dress.
Since Tameka's date is Javier, and Anthony's date was not wearing a
white dress. Sophia's date is Derrick.
And of course, Diana's dress is not white or rose so of course it is
lilac. Diana's date is Anthony.

Javar is taking Tameeka, who has on rose. Anthony is taking Diana who has on
Lilac. Derrick is taking Sophia whom has on white.

This problem required alot of thinking. So first I read the problem through a
couple of times and came up with a strategy to solve it. First I seperated the
coulumns by boys and what their date had on and girls and what they had on. So
it looked like this:

Sophia:White           Javar: rose

Tameeka: not Lilac     Anthony: not white

Diana:(nothing given)  Derrick: not Tameeka

When I put it in a table where i could see all the information I realized
something. I realized that If Sophia is wearing white and Tameeka is not
wearing Lilac. Then Tameeka must be wearing rose. This is because she can't be
wearing White, because Sophia is wearing white. It was given that she is not
wearing Lilac then the only color left is Rose. I then went back to my table
and saw that Javar's date has on a rose dress. Since Tameeka has on Rose then
she is Javar's date. This also gave us information about Diana. It was given
that Sophia has on white, so since we know now that Tameeka has on rose, the
only color left is Lilac. So Diana must have on Lilac. With this new
information I updated my table.

Sophia: white      Javar: Tameeka

Tameeka: Rose      Anthony: not Tameeka or Sophia

Diana: Lilac       Derrick: not Tameeka

Anthony's date cant be Tameeka because that is Javar's date, and it cant be
Sophia because it was stated in the begging that Anthony's date did not have
on white, so his date must be Diana. If Anthony's date is Diana the only girl
left for Derrick is Sophia. So now updated my table look like this:

Sophia: white, Derrick
Diana: lilac, Anthony
Tameeka: rose, Javar

To make sure this made sense i checked it over with the original criteria to
make sure it made sense.

Derrick's date is not Tameka.(no it's Sophia)
Anthony's date is not wearing a white dress.( no she's wearing Lilac)
Javiar's date is wearing a rose dress. (Tameeka is wearing rose)
Tameka is not wearing a lilac dress. (no she is wearing rose)
Sophia is wearing a white dress. (yes she is)

It all checks out, therefore my answer must be right.

Anthony is with Diane, who is wearing a lilac dress. Derrick is with
Sophia who is wearing a white dress. Javier is with Tameka who is
wearing a rose colored dress.

To clearly figure out my answer i used charts that looked like this

       Diane Sophia Tameka
Anthony  /      x      x *date not wearing white
Derrick  x      /      x
Javier   x      x      / *date wearing rose

      Lilac Rose White
Diane   /     x    x
Sophia  x     x    /
Tameka  x     /    x

Interpretation: Tameka is not wearing lilac so i crossed off this
choice for her. Sophia is wearing white, so i marked this and crossed
off the other two choices. This leaves rose as Tameka's only possible
dress color and then lilac as Diane's only choice.

Derrick's date is not Tameka so i crossed her off for him. I had also
made notes of the fact that Anthony's date wasn't wearing white and
that Javier's date was wearing rose. So, Javier's date is Tameka. And
This leaves only Diane as an option for Anthony and then Sophia as
the only choice for Derrick.

See below.

My Answer: Tameka is going with Javiar in a rose dress. Sophia is going with Derrick in a white dress. Diana is going with Anthony in a lilac dress.

---

Setting Up: This problem requires the solver to use deductive reasoning. So from the facts that I am given I can solve the problem. The best way to solve these problems is to set up a grid/table and mark off facts as you are given. The chart will have the 3 girls in the first column because the girls will choose a male to with and a dress to go with:

	Anthony	Derrick	Javiar	Lilac	Rose	White
Tameka
Sophia
Diana

---

Now with the first fact we are given we can already put an X mark where Derrick and Tameka's columns and rows cross because "Derrick's date is not Tameka."

	Anthony	Derrick	Javiar	Lilac	Rose	White
Tameka		X
Sophia
Diana

---

Now with the fourth fact we can put an X mark where Tameka and Lilac meet because "Tameka is not wearing a lilac dress.

	Anthony	Derrick	Javiar	Lilac	Rose	White
Tameka		X		X
Sophia
Diana

---

Now with the last fact I can put a O where Sophia and White are because "Sophia is wearing a white dress." Note that more X's will be placed because if Sophia is taking a white dress than Tameka and Diana cannot take a white dress.

	Anthony	Derrick	Javiar	Lilac	Rose	White
Tameka		X		X		X
Sophia				X	X	O
Diana						X

---

For Tameka, since all she is not wearing the Lilac or White dress she must be wearing the Rose dress. With all this we can also see that Diana is wearing a Lilac dress.

	Anthony	Derrick	Javiar	Lilac	Rose	White
Tameka		X		X	O	X
Sophia				X	X	O
Diana				O	X	X

---

Now with the second fact we can put an X mark where Anthony and Sophia meet because "Anthony's date is not wearing a white dress" and sad to say Sophia is.

	Anthony	Derrick	Javiar	Lilac	Rose	White
Tameka		X		X	O	X
Sophia	X			X	X	O
Diana				O	X	X

---

Now with the third fact, "Javiar's date is wearing a rose dress," we see that Javiar's date is Tameka because she is the one wearing the rose dress.

	Anthony	Derrick	Javiar	Lilac	Rose	White
Tameka	X	X	O	X	O	X
Sophia	X		X	X	X	O
Diana			X	O	X	X

---

Now I can fill in the holes because Sophia can only go with Derrick and that leaves Diana with Anthony:

	Anthony	Derrick	Javiar	Lilac	Rose	White
Tameka	X	X	O	X	O	X
Sophia	X	O	X	X	X	O
Diana	O	X	X	O	X	X

---

Finishing: Now with all the table finished we have that: (GIRL-BOY-DRESS)

Tameka-Javiar-Rose

Sophia-Derrick-White

Diana-Anthony-Lilac

---

Reflection: This problem was pretty much not about math, but more logic. It was fun to solve it and these problems are challenging, yet they have little math except the deductive reasoning, which you really do not know you are using. I am sure the answer is reasonable: all facts match up.

62 students received credit this week.

Fazl Abdi, age 16 - Science High School, Newark, NJ
Jorge Abrantes, age 16 - Science High School, Newark, NJ
Doyin Aderinto, age 14 - Science High School, Newark, NJ
Kristen Afonso, age 17 - Science High School, Newark, NJ
Ricky Ayala, age 15 - Science High School, Newark, NJ
Saburah Benson, age 17 - Science High School, Newark, NJ
Lavada Berger, age 15 - Science High School, Newark, NJ
Thomas Billups, age 15 - Malcolm X Shabazz High School, Newark, NJ
Edison Brito, age 14 - Science High School, Newark, NJ
Christina Brown, age 15 - Science High School, Newark, NJ
Mark Anthony Capetillo, age 16 - Science High School, Newark, NJ
Mark Cerqueira, age 15 - Science High School, Newark, NJ
Shante Coleman, age 15 - Science High School, Newark, NJ
Dominique Cummings, age 18 - Essex County Vocational-Technical High School, Newark, NJ
Susan Da Silva, age 17 - Science High School, Newark, NJ
Erick Delgado, age 16 - Science High School, Newark, NJ
Bruce Dias, age 16 - Science High School, Newark, NJ
Frank Evaristo, age 17 - Science High School, Newark, NJ
Ayodele Falae, age 17 - Science High School, Newark, NJ
Rejane Ferreira, age 16 - Science High School, Newark, NJ
Brittney Highsmith, age 15 - Science High School, Newark, NJ
Danny Jerez, age 15 - Science High School, Newark, NJ
Jason Johnson, age 18 - Malcolm X Shabazz High School, Newark, NJ
Akeem Joseph, age 16 - Science High School, Newark, NJ
Kayetan Krayewski, age 16 - Science High School, Newark, NJ
Robert Linares, age 17 - Science High School, Newark, NJ
Miguel Lopez, age 16 - Science High School, Newark, NJ
Hector Melendez, age 16 - Science High School, Newark, NJ
Janeli Melendez, age 16 - Science High School, Newark, NJ
Omar Mercado, age 16 - Science High School, Newark, NJ
Monique, average age 18 - Essex County Vocational-Technical High School, Newark, NJ
Hawwa Muhammad, age 14 - Science High School, Newark, NJ
Jonathan Muņoz, age 16 - Science High School, Newark, NJ
Olga Neradovshikh, age 15 - Science High School, Newark, NJ
Erick Nunez, age 15 - Science High School, Newark, NJ
Eruore Oboh, age 16 - Science High School, Newark, NJ
Poliana Oliveira, age 16 - Science High School, Newark, NJ
Wendy Orellana, age 15 - Science High School, Newark, NJ
Nancy Pais, age 14 - Science High School, Newark, NJ
Shelly Paredes, age 18 - Essex County Vocational-Technical High School, Newark, NJ
Stephanie Pereira, age 17 - Science High School, Newark, NJ
Victoria Petrovski, age 15 - Science High School, Newark, NJ
Kelly Porter, age 15 - Science High School, Newark, NJ
Susana Pouso, age 15 - Science High School, Newark, NJ
Javana Rhodes, age 15 - Science High School, Newark, NJ
Danny Sagal, age 16 - Essex County Vocational-Technical High School, Newark, NJ
Kristina Salvatoriello, age 16 - Science High School, Newark, NJ
Jose Santiago, age 14 - Science High School, Newark, NJ
Jessica Santos, age 14 - Science High School, Newark, NJ
Begum Siddiqua, age 14 - Science High School, Newark, NJ
Rokeya Siddiqua, age 16 - Science High School, Newark, NJ
Thiago Siqueira, age 16 - Science High School, Newark, NJ
Arooj Siraj, age 14 - Science High School, Newark, NJ
Richard Smith, age 16 - Malcolm X Shabazz High School, Newark, NJ
Theresa Thomas, age 15 - Science High School, Newark, NJ
Joffre Ulloa, age 15 - Science High School, Newark, NJ
Jo-Anis Vazquez, age 14 - Science High School, Newark, NJ
Priscilla Vazquez, age 17 - Essex County Vocational-Technical High School, Newark, NJ
Susana Vieira, age 14 - Science High School, Newark, NJ
Laquita Webb, age 17 - Science High School, Newark, NJ
Ned Wogwugwu, age 16 - Science High School, Newark, NJ
Su-Ling Wong, age 16 - Science High School, Newark, NJ

View most of the solutions submitted by the students above