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

Revision as of 19:20, 11 March 2021

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

$\binom{11}{2} = 55$ We need to subtract 5 since $2^10 - 2^0, 2^1, 2^2, 2^3, 2^4$ don't work. $55-5=\boxed{050}$ ~hansenhe

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 ==Solution==
-<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
+<math>\binom{11}{2} = 55</math> We need to subtract 5 since <math>2^10 - 2^0, 2^1, 2^2, 2^3, 2^4</math> don't work. <math>55-5=\boxed{050}</math> ~hansenhe
 ==See also==

2021 AIME I (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
All AIME Problems and Solutions