# What is the minimum number of letters that John has to send to be sure that Peter receives his letter

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John wants to send a letter to Peter, who lives on Tesla Street.
John doesn't remember the house number. However, he knows that it has 4 digits, it is a multiple of 5 and 7 and that the last digit is 0. What is the minimum number of letters that John has to send to be sure that Peter receives his letter?

posted Aug 29

so the last digit is zero which means it is a multiple of 10 and therefore is already divisible by 5
and also as it is a multiple of 7. So it is a multiple 70.
assuming the first digit can be zero we will start from 0070 as no house has a number 0000
the closest number under 10000 divisible by 70 is 9940

using term = a +(n-1)d
9940 = 70 +(n-1)70
9940/70 =1+ n-1
n = 142

so the last digit is zero which means it is a multiple of 10 and therefore is already divisible by 5
and also as it is a multiple of 7. So it is a multiple 70.
assuming the first digit cannot be zero we will start from 1050
the closest number under 10000 divisible by 70 is 9940

using term = a +(n-1)d
9940 = 1050 +(n-1)70
994 -105 = (n-1)*7
n-1 = 889/7
n = 128

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+1 vote

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