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Omni-MATH / Let a,b,c,d,e,f be integers selected from the set {1,2,…,100}, uniformly and at random with replacement. Set M=a+2b+4c+8d+16e+32f. What is the expected value of the remainder when …

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problem

Let a,b,c,d,e,fa, b, c, d, e, f be integers selected from the set {1,2,…,100}\{1,2, \ldots, 100\}, uniformly and at random with replacement. Set M=a+2b+4c+8d+16e+32fM=a+2 b+4 c+8 d+16 e+32 f. What is the expected value of the remainder when MM is divided by 64?
Plain-text mathematical notation (without MathML)
Let a,b,c,d,e,f be integers selected from the set {1,2,…,100}, uniformly and at random with replacement. Set M=a+2b+4c+8d+16e+32f. What is the expected value of the remainder when M is divided by 64?
Original LaTeX notation
Let $a, b, c, d, e, f$ be integers selected from the set $\{1,2, \ldots, 100\}$, uniformly and at random with replacement. Set $M=a+2 b+4 c+8 d+16 e+32 f$. What is the expected value of the remainder when $M$ is divided by 64?

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task_id
08dc0743-2ab1-5657-8f26-5d20bd3bbc4c
task_key
test--08dc0743-2ab1-5657-8f26-5d20bd3bbc4c
task_revision_id
1
config / split
/ test

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