Difference between revisions of "1988 AJHSME Problems/Problem 4"
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− | ==Solution== | + | ==Solution 1== |
If, for a moment, we disregard the white squares, we notice that the number of black squares in each row increases by 1 continuously as we go down the pyramid. | If, for a moment, we disregard the white squares, we notice that the number of black squares in each row increases by 1 continuously as we go down the pyramid. | ||
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Subtracting the number of white squares from the number of black squares... | Subtracting the number of white squares from the number of black squares... | ||
<cmath>1 + 2 + \cdots + 7 + 8 - (1 + 2 + \cdots + 7) = 8 \Rightarrow (B)</cmath> | <cmath>1 + 2 + \cdots + 7 + 8 - (1 + 2 + \cdots + 7) = 8 \Rightarrow (B)</cmath> | ||
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+ | ==Solution 2== | ||
+ | It is simple to notice that in each and every row, there is always one more black square than the white squares. Since there are <math>8</math> rows, there are <math>8</math> more black squares than the white squares. <math>8\rightarrow \boxed{\text{B}}</math> | ||
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+ | ~sakshamsethi | ||
+ | (Edited by Zack2008) | ||
==See Also== | ==See Also== | ||
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{{AJHSME box|year=1988|num-b=3|num-a=5}} | {{AJHSME box|year=1988|num-b=3|num-a=5}} | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
+ | {{MAA Notice}} |
Latest revision as of 10:14, 31 July 2020
Contents
Problem
The figure consists of alternating light and dark squares. The number of dark squares exceeds the number of light squares by
Solution 1
If, for a moment, we disregard the white squares, we notice that the number of black squares in each row increases by 1 continuously as we go down the pyramid. Thus, the number of black squares is .
Same goes for the white squares, except it starts a row later, making it .
Subtracting the number of white squares from the number of black squares...
Solution 2
It is simple to notice that in each and every row, there is always one more black square than the white squares. Since there are rows, there are more black squares than the white squares.
~sakshamsethi (Edited by Zack2008)
See Also
1988 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.