Difference between revisions of "1996 AIME Problems/Problem 1"
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\end{tabular}</math> | \end{tabular}</math> | ||
− | <math>x+19+96=x+1+c\Rightarrow c=19+96-1=114</math> | + | <center><math>\begin{eqnarray*}x+19+96=x+1+c\Rightarrow c=19+96-1=114,\ 114+96+a=x+1+114\Rightarrow a=x-95\end{eqnarray*}</math></center> |
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<math>\begin{tabular}[t]{|c|c|c|} | <math>\begin{tabular}[t]{|c|c|c|} | ||
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\end{tabular}</math> | \end{tabular}</math> | ||
− | <math>19+x-95+d=x+d-76=115+x\Rightarrow d=191 | + | <center><math>\begin{eqnarray*}19+x-95+d=x+d-76=115+x\Rightarrow d=191,\ 114+191+e=x+115\Rightarrow e=x-190,\ 3x-285=x+115\Rightarrow 2x=400\Rightarrow x=\boxed{200} \end{eqnarray*}</math></center> |
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== See also == | == See also == | ||
{{AIME box|year=1996|before=First Problem|num-a=2}} | {{AIME box|year=1996|before=First Problem|num-a=2}} |
Revision as of 10:55, 28 February 2008
Problem
In a magic square, the sum of the three entries in any row, column, or diagonal is the same value. The figure shows four of the entries of a magic square. Find .
Solution
Let's make a table.
See also
1996 AIME (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |