Difference between revisions of "PaperMath’s sum"
(→Notes) |
(→Notes) |
||
Line 31: | Line 31: | ||
==Notes== | ==Notes== | ||
− | Papermath’s sum was named by the aops user Papermath, after noticing it in a solution to an AMC 12 problem. The name is not widely used due to | + | Papermath’s sum was named by the aops user Papermath, after noticing it in a solution to an AMC 12 problem. The name is not widely used due to this being a whimsical statement. |
==See also== | ==See also== |
Revision as of 23:26, 19 December 2024
Contents
[hide]PaperMath’s sum
Papermath’s sum states,
Or
For all real values of , this equation holds true for all nonnegative values of
. When
, this reduces to
Proof
First, note that the part is trivial multiplication, associativity, commutativity, and distributivity over addition,
Observing that
and
concludes the proof.
Problems
AMC 12A Problem 25
For a positive integer and nonzero digits
,
, and
, let
be the
-digit integer each of whose digits is equal to
; let
be the
-digit integer each of whose digits is equal to
, and let
be the
-digit (not
-digit) integer each of whose digits is equal to
. What is the greatest possible value of
for which there are at least two values of
such that
?
Notes
Papermath’s sum was named by the aops user Papermath, after noticing it in a solution to an AMC 12 problem. The name is not widely used due to this being a whimsical statement.