Difference between revisions of "2021 AIME I Problems/Problem 3"

Revision as of 18:20, 11 March 2021

Find the number of positive integers less than $1000$ that can be expressed as the difference of two integral powers of $2.$

$\binom{11}{2} = 55 \implies 55 - 5 = 50$ . We need to subtract 5 since $2^10 - 2^0, 2^1, 2^2, 2^3, 2^4$ don't work. ~hansenhe

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 ==Solution==
-<math>9+8+7+6+5+5+4+3+2+1=\boxed{50}</math>
+<math>\binom{11}{2} = 55 \implies 55 - 5 = 50</math>. We need to subtract 5 since <math>2^10 - 2^0, 2^1, 2^2, 2^3, 2^4</math> don't work. ~hansenhe
 ==See also==
 {{AIME box|year=2021|n=I|num-b=2|num-a=4}}

2021 AIME I (Problems • Answer Key • Resources)
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