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# How many three-digit positive integers have at least one prime digit?

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162
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+269

How many three-digit positive integers have at least one prime digit?

So I thought it would be easier to start counting the numbers that do not have any prime digits.

Aug 2, 2022

#1
+124708
+2

Here's my best attempt  (I'm not great at these counting problems !!! )

Non-prime digits = (0, 1, 4, 6, 8, 9 )

Number of three digit numbers not having any prime digits

Hundreds place  = (Choose  any  one of the digits 1,4,6,8,9) =  C(5,1) = 5

Tens place  = ( Choose any one of the digits 0,1,4,6,8,9) = C(6,1)  = 6

Ones place = (Choose any one  of the digits 0,1,4,6,8,9) = C(6,1)  = 6

So   5 * 6 * 6 =    180 have no prime digits

So

900  three digit numbers -  180 with no prime digits  =

720  have at least one prime digit

Aug 2, 2022
edited by CPhill  Aug 2, 2022
edited by CPhill  Aug 2, 2022
#2
+2602
0

There are $$900 - 5 \times 6 \times 6 = \color{brown}\boxed{720}$$ numbers with at least 1 prime digit.

Aug 2, 2022
#3
+124708
+1

DUH!!!

CPhill  Aug 2, 2022