Transcript Is It a Digit

Is It a Digit?
IMP
SOLVE IT!
There are five empty boxes shown here labeled 0 through 4.
0
1
2
3
4
Your task is to put a digit 0 through 4 inside each of the
boxes so that certain conditions hold:
0
1
2
3
4
 The digit you put in the box labeled “0” must be the same
as the number of 0’s you use.
 The digit you put in the box labeled “1” must be the same
as the number of 1’s you use.
 The digit you put in the box labeled “2” must be the same
as the number of 2’s you use, and so on…
Additional Information
What to do
 You are allowed to use
the same digit more than
once.
 You may want to make
several copies of the set
of boxes in order to try
the various combinations
of digits.
What Not to Do
 Here is an example of an
incorrect way to fill the
boxes.
2
3
1
2
2
 This is incorrect for many
reasons. For instance, there is
a 1 in the box labeled “2”, but
there is more than one 2 in the
boxes…..
POW 1
A Digital
Proof
Once you have solved the problem in Is it a Digit?,
your task is to prove that you have all the
solutions.
Write Up
1.
Problem Statement: Explain the problem from
Is it a Digit?
2.
Process: Based on your notes, describe how
you went about finding all the solutions to Is it
a Digit? And how you decided that you had
them all.
3.
Solutions: List all solutions you found for the Is
it a Digit? Then write a careful and detailed
proof that there are no solutions to Is it a Digit?
other than those listed.
4.
Evaluation
5.
Self-assessment
 Warning!!!!!!
 The answer(s) follow on the
following slide.
 The order of the numbers should be
2
1
2
0
0
 The proof that the solution is unique consists fo
eliminating all other possibilities. However, there
are so many possibilities (55 or 3125) the other
cases need to be eliminated in an organized and
systematic way.
 However, once 3 and 4 are eliminated, a proof
could be made by showing the 33 or 27
possibilities.
 Also a proof can be shown that the digits must be
equal to 5.