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Math Challenge I-A Spring 2019 Week 4

 
 
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Math Challenge I-A Spring 2019 Week 4
by Amy T - Saturday, March 23, 2019, 8:37 PM
 

Find a four-digit multiple of 1111 consisting of entirely 33s and 55s. Is there only one?

 
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Re: Math Challenge I-A Spring 2019 Week 4
by peter zhao - Sunday, March 24, 2019, 12:37 PM
 

Since the rule for 11 is the alternating sum being 0, the possible numbers are 3355 and 5533. :D

 
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Picture of Amy T
回复: Re: Math Challenge I-A Spring 2019 Week 4
by Amy T - Monday, March 25, 2019, 7:00 PM
 

gee, thanks

 
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Re: Math Challenge I-A Spring 2019 Week 4
by David Reynoso - Monday, March 25, 2019, 10:22 AM
 

Proceed similar to example 4.4. As they mention above, you want to use the fact that a number is a multiple of $11$ if the alternating sum of its digits is a multiple of $11$ (Note this does not mean the alternating sum must be $0$, it can be any multiple of $11$).

 
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