Here is a collection of combinatorics problems and solutions for new ideas:
P1Connie finds a whiteboard that has magnet letters spelling MISSISSIPPI on it. She can rearrange the letters, in which identical letters are indistinguishable. If she uses all the letters and does not want to place any Is next to each other, how many distinct rearrangements are possible?
S1 (Gap Method)We first arrange the
M,P,S and later put the
Is. Ways to arrange the
M,P,S 
. We have
places to choose form and
way to arrange the
Is in it. Thus the final answer is
.Carson is planning a trip for
people. Let
be the number of cars that will be used and
be the number of people per car. What is the smallest value of
such that there are exactly
possibilities for
and
so that
is an integer,
, and exactly one person is left without a car?
Ofcourse
. Now
. As there are
possible values for
(and the corresponding values of
) thus the total number of factors of
is
. can be of the form
or
. We bash to find the least is possible in the second case with
and
thus resulting the final
in being
.Observing
was quite natural. Now the main thing is observing that
has
factors. This gives us an idea that whenever in case of product and stuff with a certain quantity given, we should check for factors and stuff.
This post has been edited 1 time. Last edited by SomeonecoolLovesMaths, Dec 6, 2024, 4:18 PM
by SomeonecoolLovesMaths, Dec 4, 2024, 3:52 PM 
.
places to choose form and 
way to arrange the Is in it. Thus the final answer is 
.
people. Let 
be the number of cars that will be used and 
be the number of people per car. What is the smallest value of 
possibilities for 
,
.
.
is 
.
or 
.
and 
thus resulting the final 
.
was quite natural. Now the main thing is observing that 
March 2025
February 2025