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Math Challenge I-A Spring 2019 Week 4

 
 
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Math Challenge I-A Spring 2019 Week 4
TAmy - 2019年03月23日 Saturday 20:37
 

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
zhaopeter - 2019年03月24日 Sunday 12:37
 

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

 
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回复: Re: Math Challenge I-A Spring 2019 Week 4
TAmy - 2019年03月25日 Monday 19:00
 

gee, thanks

 
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ReynosoDavid的头像
Re: Math Challenge I-A Spring 2019 Week 4
ReynosoDavid - 2019年03月25日 Monday 10:22
 

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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