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- Thread starter Joe_1234
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2×3×3×3=54, is this correct sir? I am confused since 51 is the key answerWhat have you tried, and where are you stuck?

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(1) First digit is 3:

Then the rest of the numbers must come from the list: 2, 2, 3, 3, 4, 4, 4, 4

Therefore we may choose any 3-digit sequence except 222 and 333 for the rest of the digits. This shows there are:

\(\displaystyle N_1=3^3-2=25\)

numbers in this case.

(2) First digit is 4:

Then the rest of the numbers must come from the list 2, 2, 3, 3, 3, 4, 4, 4

Therefore we may choose any 3-digit sequence except 222 for the rest of the digits. This shows there are:

\(\displaystyle N_2=3^3-1=26\)

numbers in this case.

Hence, the total number is:

\(\displaystyle N=N_1+N_2=51\)

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Thank you sir

(1) First digit is 3:

Then the rest of the numbers must come from the list: 2, 2, 3, 3, 4, 4, 4, 4

Therefore we may choose any 3-digit sequence except 222 and 333 for the rest of the digits. This shows there are:

\(\displaystyle N_1=3^3-2=25\)

numbers in this case.

(2) First digit is 4:

Then the rest of the numbers must come from the list 2, 2, 3, 3, 3, 4, 4, 4

Therefore we may choose any 3-digit sequence except 222 for the rest of the digits. This shows there are:

\(\displaystyle N_2=3^3-1=26\)

numbers in this case.

Hence, the total number is:

\(\displaystyle N=N_1+N_2=51\)