What theorems and principles that you believe are employed to solve the following riddle You’ve all been captured and br
Posted: Fri Apr 29, 2022 11:02 am
What theorems and principles that you believe are employed to
solve the following riddle
You’ve all been captured and brought to the ancient Colosseum
for their deadly entertainment before you’re thrown into the
dungeon. You see many numbered hallways leading outside, but each
exit is blocked by an electric barrier with a combination keypad.
You learn that one of you will be allowed to try to escape by
passing a challenge while everyone else will be fed to the mutant
salamanders the following day. With her perfect logical
reasoning, Sarah is the obvious choice. You hand her a
concealed audio transmitter so that the rest of you can listen
along as Sarah is led away. You hear her footsteps echo
through one of the hallways and then stop. A voice announces
that she must enter a code consisting of three positive whole
numbers in ascending order, so the second number is greater than or
equal to the first and the third is greater than or equal to the
second. She may ask for up to three clues, but she'll be
thrown back into the dungeon if she makes a wrong guess or says
anything else. For the first clue, the voice says the product of
the three numbers is 36. When Sarah asks for the
2nd clue, the voice says the sum of the numbers is the
same as the number of the hallway she entered. There’s a long
silence. You’re sure Sarah remembers the hallway number, but
there’s no way for you to know it, and she can’t say it out loud.
If Sarah could enter the passcode, she would, but instead, she asks
for the third clue. The voice announces that the largest number
appears only once in the combination moments later. The buzz of the
electric barrier stops for a few seconds. You realize that Sarah
has escaped; unfortunately, her transmitter is longer in range, so
that’s all the information you get. Can you find the
solution? Hallway number, but you decide to start from the
beginning anyway. From the first clue, you work out all of the
possible combinations that come out to a product of 36. One of
these must be right, but which one? Now comes the hard part. Even
though you don’t know which number you’re looking for, you decide
to calculate the sum of each combination number. All but two of the
sums are unique, and if the hallway number had matched any of
these, Sarah would have known the correct combination right then
and there without asking for the third clue. Since she did ask for
the clue, the hallway number must have matched the only some that
appears more than once in the list 13, but which of the two
combinations that add up to 13 is correct 1, 6, 6, or 2, 2, 9?
That’s where the third clue comes in since it tells us that the
largest number must be unique to 29 must be the code when night
falls you and the others escaped through hallway 13 and rejoins are
outside you freed yourselves through math and logic now it’s time
to free the rest of the world.
solve the following riddle
You’ve all been captured and brought to the ancient Colosseum
for their deadly entertainment before you’re thrown into the
dungeon. You see many numbered hallways leading outside, but each
exit is blocked by an electric barrier with a combination keypad.
You learn that one of you will be allowed to try to escape by
passing a challenge while everyone else will be fed to the mutant
salamanders the following day. With her perfect logical
reasoning, Sarah is the obvious choice. You hand her a
concealed audio transmitter so that the rest of you can listen
along as Sarah is led away. You hear her footsteps echo
through one of the hallways and then stop. A voice announces
that she must enter a code consisting of three positive whole
numbers in ascending order, so the second number is greater than or
equal to the first and the third is greater than or equal to the
second. She may ask for up to three clues, but she'll be
thrown back into the dungeon if she makes a wrong guess or says
anything else. For the first clue, the voice says the product of
the three numbers is 36. When Sarah asks for the
2nd clue, the voice says the sum of the numbers is the
same as the number of the hallway she entered. There’s a long
silence. You’re sure Sarah remembers the hallway number, but
there’s no way for you to know it, and she can’t say it out loud.
If Sarah could enter the passcode, she would, but instead, she asks
for the third clue. The voice announces that the largest number
appears only once in the combination moments later. The buzz of the
electric barrier stops for a few seconds. You realize that Sarah
has escaped; unfortunately, her transmitter is longer in range, so
that’s all the information you get. Can you find the
solution? Hallway number, but you decide to start from the
beginning anyway. From the first clue, you work out all of the
possible combinations that come out to a product of 36. One of
these must be right, but which one? Now comes the hard part. Even
though you don’t know which number you’re looking for, you decide
to calculate the sum of each combination number. All but two of the
sums are unique, and if the hallway number had matched any of
these, Sarah would have known the correct combination right then
and there without asking for the third clue. Since she did ask for
the clue, the hallway number must have matched the only some that
appears more than once in the list 13, but which of the two
combinations that add up to 13 is correct 1, 6, 6, or 2, 2, 9?
That’s where the third clue comes in since it tells us that the
largest number must be unique to 29 must be the code when night
falls you and the others escaped through hallway 13 and rejoins are
outside you freed yourselves through math and logic now it’s time
to free the rest of the world.