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The product of the digits of 3214 is 24. How many distinct four-digit positive integers are such that the product of their digits equals 12?

 Feb 28, 2020
 #1
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1126  1134  1143  1162  1216  1223  1232  1261  1314  1322  1341  1413  1431  1612  1621  2116  2123  2132  2161  2213  2231  2312  2321  2611  3114  3122  3141  3212  3221  3411  4113  4131  4311  6112  6121  6211  Total =  36

 Feb 28, 2020
 #2
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12 =2 x 2 x 4, or:

12 =3 x 4, or:

12 =2 x 6

Note: I don't think that you can have 4 DISTINCT digits whose product = 12. There must be "repeats" !!

 Feb 28, 2020

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