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Omni-MATH / Suppose that R,S and T are digits and that N is the four-digit positive integer 8RST. That is, N has thousands digit 8, hundreds digit R, tens digits S, and ones (units) digit T, w…

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problem

Suppose that R,SR, S and TT are digits and that NN is the four-digit positive integer 8RST8 R S T. That is, NN has thousands digit 8, hundreds digit RR, tens digits SS, and ones (units) digit TT, which means that N=8000+100R+10S+TN=8000+100 R+10 S+T. Suppose that the following conditions are all true: - The two-digit integer 8R8 R is divisible by 3. - The three-digit integer 8RS8 R S is divisible by 4. - The four-digit integer 8RST8 R S T is divisible by 5. - The digits of NN are not necessarily all different. What is the number of possible values for the integer NN?
Plain-text mathematical notation (without MathML)
Suppose that R,S and T are digits and that N is the four-digit positive integer 8RST. That is, N has thousands digit 8, hundreds digit R, tens digits S, and ones (units) digit T, which means that N=8000+100R+10S+T. Suppose that the following conditions are all true: - The two-digit integer 8R is divisible by 3. - The three-digit integer 8RS is divisible by 4. - The four-digit integer 8RST is divisible by 5. - The digits of N are not necessarily all different. What is the number of possible values for the integer N?
Original LaTeX notation
Suppose that $R, S$ and $T$ are digits and that $N$ is the four-digit positive integer $8 R S T$. That is, $N$ has thousands digit 8, hundreds digit $R$, tens digits $S$, and ones (units) digit $T$, which means that $N=8000+100 R+10 S+T$. Suppose that the following conditions are all true: - The two-digit integer $8 R$ is divisible by 3. - The three-digit integer $8 R S$ is divisible by 4. - The four-digit integer $8 R S T$ is divisible by 5. - The digits of $N$ are not necessarily all different. What is the number of possible values for the integer $N$?

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Source and history

task_id
2c97108e-320d-5a81-bd99-a671ba6e239f
task_key
test--2c97108e-320d-5a81-bd99-a671ba6e239f
task_revision_id
1
config / split
/ test

Official source

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