[Guest]

Sam leaves in a tower. One day due to the power shortage, Sam and other passengers cannot use the elevator. They had no choice but to walk from the ground floor to their floor by using staircase. Being a helpful teenager, Sam helped an old nanny to carry her bags to the floor she stay, Sam walked fast, Nanny walked slowly and here the story goes.

Sam walked up with consistent speed to certain level. He then realized he forgot to ask the nanny which floor she stays. He walked down again (same speed) and met her exactly at the floor number half of the floor number where Sam turned back. After confirming the floor number (and lot number, of course) with the nanny, Sam walked up again. After 2 floors he walked up, he remember he should check his mailbox at the ground floor. Understood the nanny will not reach her floor faster than Sam would, Sam walked down again, passing by the nanny and reached the ground floor and checked his mailbox. He quickly took all the letters and walked up again. This time, they met again at exact floor level, which the number is one-quarter of the floor number where Sam is staying.

Sam continued walk to the floor he stays, which is 3 floors below the top floor. He threw all the letters in and walked down to the floor where the nanny stays. Both of them reach the floor the nanny stays at the same time.

Assumption, if Sam and the nanny walked in their speed consistently, and the time for Sam seeking for the floor number, checking the mailbox, and throwing the letter in the house are negligible; How many floor (at least) does the tower has?

[Guest]

Assumption, if Sam and the nanny walked in their speed consistently, and the time for Sam seeking for the floor number, checking the mailbox, and throwing the letter in the house are negligible; How many floor (at least) does the tower has?

Tough hunt!

The tower must have at least 19 floors, the Nanny lives at the 10th, Sam at the 16th

[Guest]

Sam leaves in a tower. One day due to the power shortage, Sam and other passengers cannot use the elevator. They had no choice but to walk from the ground floor to their floor by using staircase. Being a helpful teenager, Sam helped an old nanny to carry her bags to the floor she stay, Sam walked fast, Nanny walked slowly and here the story goes.

Sam walked up with consistent speed to certain level. He then realized he forgot to ask the nanny which floor she stays. He walked down again (same speed) and met her exactly at the floor number half of the floor number where Sam turned back. After confirming the floor number (and lot number, of course) with the nanny, Sam walked up again. After 2 floors he walked up, he remember he should check his mailbox at the ground floor. Understood the nanny will not reach her floor faster than Sam would, Sam walked down again, passing by the nanny and reached the ground floor and checked his mailbox. He quickly took all the letters and walked up again. This time, they met again at exact floor level, which the number is one-quarter of the floor number where Sam is staying.

Sam continued walk to the floor he stays, which is 3 floors below the top floor. He threw all the letters in and walked down to the floor where the nanny stays. Both of them reach the floor the nanny stays at the same time.

Assumption, if Sam and the nanny walked in their speed consistently, and the time for Sam seeking for the floor number, checking the mailbox, and throwing the letter in the house are negligible; How many floor (at least) does the tower has?

The tower should have 23 floors, Sam living at 20th floor and Nanny at 15th floor

[CaptainEd]

If the Ground floor is numbered 0 (European tradition), I agree with Boiling Oil. I haven't worked it out if Ground = 1 (American tradition).

[Guest]

Sam leaves in a tower. One day due to the power shortage, Sam and other passengers cannot use the elevator. They had no choice but to walk from the ground floor to their floor by using staircase. Being a helpful teenager, Sam helped an old nanny to carry her bags to the floor she stay, Sam walked fast, Nanny walked slowly and here the story goes.

Sam walked up with consistent speed to certain level. He then realized he forgot to ask the nanny which floor she stays. He walked down again (same speed) and met her exactly at the floor number half of the floor number where Sam turned back. After confirming the floor number (and lot number, of course) with the nanny, Sam walked up again. After 2 floors he walked up, he remember he should check his mailbox at the ground floor. Understood the nanny will not reach her floor faster than Sam would, Sam walked down again, passing by the nanny and reached the ground floor and checked his mailbox. He quickly took all the letters and walked up again. This time, they met again at exact floor level, which the number is one-quarter of the floor number where Sam is staying.

Sam continued walk to the floor he stays, which is 3 floors below the top floor. He threw all the letters in and walked down to the floor where the nanny stays. Both of them reach the floor the nanny stays at the same time.

Assumption, if Sam and the nanny walked in their speed consistently, and the time for Sam seeking for the floor number, checking the mailbox, and throwing the letter in the house are negligible; How many floor (at least) does the tower has?

The tower has 27 floors (at least). The nanny lives at 15th floor and Sam lives at 24th floor.

Edited March 12, 2009 by huxiaoxia

[Guest]

If the Ground floor is numbered 0 (European tradition), I agree with Boiling Oil. I haven't worked it out if Ground = 1 (American tradition).

The way the floors are numbered shouldn't affect how many floors there actually are though. If, for example, you work it out for ground = 0, and you figure the top to be floor 20, then the answer is the same for ground = 1 (top is 21). Numbering differences shouldn't affect the number of floors.

[Guest]

Edit: I just wanted to agree with Inzuri, who hadn't posted when I started writing my response. The numbering system isn't really important, and in fact you can letter the floors or call them symbols if you want.

Note: I'm assuming that Jeff moves at less than infinite speed. If he moved at infinite speed, then both him and granny would live on the ground floor, and the building would have 3 other floors for a total of 4 (0 to 3).

The tower has at least 20 floors (ground being 0, top being 19).

The first situation indicates that Jeff moves 3 times the speed of granny (up double and back).

Call the first floor they meet on x and the second y. The time Jeff will take to make it to the second meeting from the first will be (assuming 1 time unit = 1 floor for granny)

(4 + x + y)/3 => up 2, down 2, down x, up y at 3x granny's speed

Time for granny to make the same trip will be

y - x

Therefore y = 2x + 2. Jeff's floor is at 4y, and the building has 3 more floors than that, so the building must have 8x + 11 floors.

Substituting the smallest reasonable value for x (1), we get that the building has 19 upper floors.

For triviality:

When Jeff subsequently reaches his floor (4y), granny will be at floor 2y. They will meet again (at granny's floor) at floor 5y/2. This gives the floor number for each meeting at 1, 4, and 10. Granny lives at 10, Jeff lives at 16, and the top floor is 19.

The first meeting being arbitrary, you could plug in any value for x above and re-calculate all the floors.

Edited March 12, 2009 by jb_riddler

[bonanova]

The way the floors are numbered shouldn't affect how many floors there actually are though. If, for example, you work it out for ground = 0, and you figure the top to be floor 20, then the answer is the same for ground = 1 (top is 21). Numbering differences shouldn't affect the number of floors.

OK for adding and subtracting floor numbers.

What about multiplying and dividing them?

[bonanova]

Edit: I just wanted to agree with Inzuri, who hadn't posted when I started writing my response. The numbering system isn't really important, and in fact you can letter the floors or call them symbols if you want.

Could the ground floor be given any number, say 13?

[CaptainEd]

Edit: I just wanted to agree with Inzuri, who hadn't posted when I started writing my response. The numbering system isn't really important, and in fact you can letter the floors or call them symbols if you want.

Note: I'm assuming that Jeff moves at less than infinite speed. If he moved at infinite speed, then both him and granny would live on the ground floor, and the building would have 3 other floors for a total of 4 (0 to 3).

The tower has at least 20 floors (ground being 0, top being 19).

The first situation indicates that Jeff moves 3 times the speed of granny (up double and back).

Call the first floor they meet on x and the second y. The time Jeff will take to make it to the second meeting from the first will be (assuming 1 time unit = 1 floor for granny)

(4 + x + y)/3 => up 2, down 2, down x, up y at 3x granny's speed

Time for granny to make the same trip will be

y - x

Therefore y = 2x + 2. Jeff's floor is at 4y, and the building has 3 more floors than that, so the building must have 8x + 11 floors.

Substituting the smallest reasonable value for x (1), we get that the building has 19 upper floors.

For triviality:

When Jeff subsequently reaches his floor (4y), granny will be at floor 2y. They will meet again (at granny's floor) at floor 5y/2. This gives the floor number for each meeting at 1, 4, and 10. Granny lives at 10, Jeff lives at 16, and the top floor is 19.

The first meeting being arbitrary, you could plug in any value for x above and re-calculate all the floors.

I agree with the math exactly, starting with floor number 1 being above the ground floor. The reason the origin matters is, the problem very clearly identifies when "floor number" is some fraction of some other "floor number". You could not replace the identities with letters.

If you disagree, then if the ground floor IS number 1, then please explain on what floor number they meet for the first time, and their relative rates of speed.

[Guest]

Well done to BoilingOil being the first person, Inzuri and jb_riddler come out with the detail calculation.

[Guest]

... He walked down again (same speed) and met her exactly at the floor number half of the floor number where Sam turned back...

...which the number is one-quarter of the floor number where Sam is staying...

You guys are right! I wasn't paying enough attention to realize this (above) from the OP. If he'd said "the floor that is halfway to" instead of the bold, then it wouldn't matter. Interesting point to consider, and I'll have to update with a more general answer, I suppose.

[Magic_luver101]

i got 21 i mabe over caulting