Video summary
In this mathematical challenge, an ant attempts to climb a staircase of nine steps following a specific pattern where it ascends two steps before sliding back down one. The problem establishes that climbing a single step takes three minutes while descending takes only two minutes. To solve the puzzle without simply multiplying by the net gain per cycle, viewers are encouraged to analyze exactly how many times the ant performs each action throughout its journey to reach the top floor.
By carefully tracing the ant's movement from the bottom, it becomes clear that the first step is climbed once because every subsequent climb involves reaching a new height before slipping back. Consequently, steps two through eight are each climbed twice as part of these cycles, while the final ninth step is reached only once at the very end and never descended upon since the goal is achieved. This logical breakdown reveals that the ant climbs a total of seventeen times (one for the first step plus sixteen from climbing the remaining eight intermediate levels twice) but descends exactly eight times between those successful ascents.
Calculating the total duration involves multiplying these frequencies by their respective time costs: seventeen upward movements take fifty-one minutes, and eight downward slips consume another sixteen minutes. Adding these two durations together results in a final answer of sixty-seven minutes required for the ant to successfully reach the ninth step. This solution demonstrates how breaking down repetitive patterns into specific counts of actions allows one to solve complex-looking problems using simple multiplication and addition rather than getting confused by the net progress per cycle.
Read the full video transcript
hello and welcome to the session in this
session we are going to solve a
mathematical
challenge an ant wants to climb the
stairs after climbing every two steps
she comes down one step if it takes 3
minutes to climb up one step and 2
minutes to come down one
step how much time will the ant take to
climb nine
steps before solving this challenge let
me give you a hint which can help you to
solve this
challenge this challenge is based on
multiplication and addition of whole
numbers this challenge also involves
mental calculations of how many steps
did the ant climb and how many steps did
she come down to solve you first
calculate the number of
steps The Ant
climed and then find the number of steps
she came
down after this use
multiplication to
find the time
taken by
the
ant to climb nine
steps so using this now try and complete
the
challenge observe the statement
carefully you may pause the video to try
it yourself
were you able to solve it let me help
you let us read the statement carefully
an ant wants to climb the stairs after
climbing every two steps she comes down
one step if it takes 3 minutes to climb
up one step and 2 minutes minutes to
come down one
step how much time will the ANS take to
climb nine steps so here we see that it
takes 3
minutes to climb up one
step and 2 minutes
to come down one
step also we are given that she
climbed nine
steps so let us first find out the
number of times she climbed up and and
the number of times she came down let us
begin with the first
step the ant climed First
Step then to the second step and then
came down one
step so now she comes back to step
one now
again she climbs step two
and step three and comes back to step
two again she
climbs step three and step four and
comes back to step
three if we continue like this we
observe that she climbs step one once
and each step from 2 to 9 twice that is
eight
stepss are climbed
twice so total number of steps she
climbed is 1 + 2 *
8 which is = 1 + 16 which is equal = to
17
steps also step 9 is the last step so
she cannot come down to step nine so she
came down to every step from 1 to 8
except at step
9 so number of steps she came down
is8 so she climbed
17
steps and came
down eight
steps now let us calculate the total
time we are given it takes 3 minutes to
climb up one step and 2 minutes to come
down one step total time taken to climb
17 steps is equal to 3
*
17 which is equal to 3 into 17 which is
equal to 51
minutes total time taken to come down
eight steps is equ
= 2 * 8 which is equal to 16
minutes so time taken to reach the n9th
step is 51
minutes plus 16
minutes which is equal to 67 minutes
wasn't that easy so with this we have
completed our
challenge hope you enjoyed it