Problem Solving

stack of boards at lumber yard, the 20th board counting from the top of the stack is immediately below the 16 th board counting from the bottom of the stack. how many boards are in the stack?

I had made a mistake,when I solved this problem

Ajith, can you please explain how you got 20 = n-14 ..?

let there be n boxes overall
let the first box be numbered 1 and let the last box be numbered n

1 n - (n-1)
2 n - (n-2)
3 n - (n-3)
.
.
15 (n-15)
20 (n-14)
.
.
.
n n

Now we want to find n

It says that box numbered 20 is below box numbered n-15
meaning box numbered 20 can also be numbered n-14
ie 20 = n-14

meaning n= 34

How did you get n-14

it says 20th is immediately below 16th counting from the bottom


Im sorry I dont follow, can you expand on it.

yvonne12 wrote:How did you get n-14

it says 20th is immediately below 16th counting from the bottom


Im sorry I dont follow, can you expand on it.

while ajith has used the variable n to solve the q ... it can also be solved intutively ....

the q says that the 20th board when counted from the top is immediately below the 16th board .. so that means there are 19 boards above the 20th board (that wuld also include the 16th board .. bcoz the 16th board is on the top of the 20th board)..... also the 16th board from the bottom wuld have 15 boards below it ( that wuld include the 20th board) ...

since there are no boards between the 16th and the 20th board ... the total no of boards is 19+15=34 ...

also check out the attachment it will help u picturize the q ...

thank you Gabriel, that was very helpful.

I am sorry not to see this till now

It is very much a counting problem where in you can count from top and the bottom.

First of all I assumed there are n boxes and started counting from the bottom but with a difference, n would be the bottom most n-1 would be 2nd last and 1 would be the topmost

I can start counting from the top also, 1, 2, .... n

Now the question says 16th box from bottom (n-15 according to first method of counting) is exacly above 20 th from top (No 20 according to 2nd method of counting).

Since both the numbering are the same 20th box from top would have 20 in it either way you count it

ie

20 = (n-15+1)

=> n= 34