Quandaries and Queries
  

 

Name: Megan

Who is asking: Student Level: Middle

Question: Use each digit 1-9 only one time each, divide the numbers into 3 groups, make one 2 digit number, one 3 digit number, and one 4 digit number. There are 6 combinations of these numbers in which you can multiply the 2 digit and 3 digit number together to get the 4 digit number (using each digit 1-9 one time each). What are they!!!!!!!!!????????????
 

 

Hi Megan,

I got 7 combinations:

12 , 483 , 5796
18 , 297 , 5346
27 , 198 , 5346
28 , 157 , 4396
39 , 186 , 7254
42 , 138 , 5796
48 , 159 , 7632A computer program does it rightaway, by checking all possibilities. There are also clever ways of eliminating possibilities, and do it by hand, but you must be careful to avoid mistakes (which is also true in programming). The mistake in claiming that there are only 6 possibilities probably comes from the fact that 5346 and 5796 both appear twice as a 4-digit number.

Claude
 
 

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