Difference between revisions of "1985 AJHSME Problem 7"
Coolmath34 (talk | contribs) (Created page with "== Problem == A "stair-step" figure is made of alternating black and white squares in each row. Rows <math>1</math> through <math>4</math> are shown. All rows begin and end w...") |
(→In-depth Solution by Boundless Brain!) |
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<math>\text{(A)}\ 34 \qquad \text{(B)}\ 35 \qquad \text{(C)}\ 36 \qquad \text{(D)}\ 37 \qquad \text{(E)}\ 38</math> | <math>\text{(A)}\ 34 \qquad \text{(B)}\ 35 \qquad \text{(C)}\ 36 \qquad \text{(D)}\ 37 \qquad \text{(E)}\ 38</math> | ||
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| + | == In-depth Solution by BoundlessBrain!== | ||
| + | https://youtu.be/6Y2SysY3U2k | ||
== Solution== | == Solution== | ||
Notice that in the <math>n</math>th row, there are <math>n</math> white squares and <math>n-1</math> black squares. So, the <math>37th</math> row will have <math>\boxed{\text{(C) 36}}</math> black squares. | Notice that in the <math>n</math>th row, there are <math>n</math> white squares and <math>n-1</math> black squares. So, the <math>37th</math> row will have <math>\boxed{\text{(C) 36}}</math> black squares. | ||
Latest revision as of 23:02, 29 June 2023
Problem
A "stair-step" figure is made of alternating black and white squares in each row. Rows 
through 
are shown. All rows begin and end with a white square. The number of black squares in the 
row is
![[asy] draw((0,0)--(7,0)--(7,1)--(0,1)--cycle); draw((1,0)--(6,0)--(6,2)--(1,2)--cycle); draw((2,0)--(5,0)--(5,3)--(2,3)--cycle); draw((3,0)--(4,0)--(4,4)--(3,4)--cycle); fill((1,0)--(2,0)--(2,1)--(1,1)--cycle,black); fill((3,0)--(4,0)--(4,1)--(3,1)--cycle,black); fill((5,0)--(6,0)--(6,1)--(5,1)--cycle,black); fill((2,1)--(3,1)--(3,2)--(2,2)--cycle,black); fill((4,1)--(5,1)--(5,2)--(4,2)--cycle,black); fill((3,2)--(4,2)--(4,3)--(3,3)--cycle,black); [/asy]](http://latex.artofproblemsolving.com/1/6/b/16bbf453deb73effcd29c04ae7b433e465c6cffd.png)
In-depth Solution by BoundlessBrain!
Solution
Notice that in the 
th row, there are white squares and 
black squares. So, the 
row will have 
black squares.
