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How many positive 3 -digit numbers A⎯⎯⎯B⎯⎯⎯C⎯⎯⎯ are such that the product of the 2 -digit numbers A⎯⎯⎯B⎯⎯⎯ and B⎯⎯⎯C⎯⎯⎯ equals A⎯⎯⎯B⎯⎯⎯C⎯⎯⎯ ?

 Mar 3, 2020
 #1
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There is one number that works: 11*10 = 110.

 Mar 3, 2020
 #2
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I read your question to mean: (A*B) * (B*C) =A*B*C. If that is the case, then we have:

 

a=1;b=0;c=0;p=0; cycle:d=a*100+b*10+c;if((a*b) *(b*c)==a*b*c, goto loop, goto next); loop:printd," ",;p=p+1; next:c++;if(c<10, goto cycle, 0);c=0;b++;if(b<10, goto cycle, 0);b=0;c=0;a++;if(a<10, goto cycle,0);print"Total = ",p

 

OUTPUT = 252 such numbers.

 Mar 3, 2020

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