Time for MATH MINUTE! (provide your favorite theme music
here).
Get out
your paper & pencil, because I have a new puzzle for you!!
Responses/Hints: PUZZLE #97 The Hunt
A. Make a list
of all of the squares of whole numbers which have 4 digits, like 322
= 1024, . . .
One
of these squared numbers shares at least one digit with each of the others.
What is it?
Here is a list of all
squared whole numbers which have 4 digits.
If
you found the number to be 6241 you are right!
B. Make a
list of all of the squares of whole numbers which have 3 digits, like 102
= 100.
None
of these squared numbers shares a digit with each of the others. Why not?
Here is a list of all
squared whole numbers which have 3 digits.
You
could go through the entire list and check each number to see that it does not
share a digit with each of the other numbers in the list, and this works, so if
you did this congratulation!
But
you could also just check a few numbers as follows.
For
example, the numbers 100, 400, and 900 in the list show that the number we need
must have 3 of the 4 numbers 1, 4, 9, and 0. Since these 3 numbers are the only
ones with a 0, it would be futile to include 0 in the desired number. This
means the number we need must have the digits 1, 4, and 9. But a quick scan of
the list shows that there are no numbers with these 3 digits. Case closed.
Have
fun!
Send
your comments, ideas and solutions before Monday to the email below, and
in the subject line be sure to put
MM in the subject line
Visit
us here online at:
http://www2.potsdam.edu/parksjm/MM1.1.htm
to see the results every Friday.
See you next time on MATH MINUTE! (theme music fades out here).