Good ol' 1001, but let's say we don't know that 1001 magic. Now since the number N ends in 5 it will be divisible by 7x11x13x5 = 5005. To go from 5005 to a six digit number starting with 6 we need to multiply by 12Y where Y has to be odd, so N will end in 5 (for y = even N would end in 0). 121 and 123 won't do it, so it's 125: 5005x125= 625625
If a number is to be completely divisible by 7, 11 and 13 and is a 6 digit number, it is also going to be divisible by 7x11x13 which is 1001. From here you don't need to follow his method if you don't want to. Even without knowing the property of a 6 digit number multiplied by 1001 having repetitive digits, you can just try to guess it with the first 2 digits and the last digit. The last digit is 5 so 1001 is multiplied with a number that ends with 5. Also, the first digit of that number also needs to be 6 for the first digit of the unknown number's first digit to be 6. And since 1001 has 4 digits and the unknown number has 6 digits, we know that 1001 is multiplied with a 3 digit number. So we are looking at a 3 digit number that starts with 6 and ends with 5. Since second digit is 2 of the unknown number is 2, we just try 2 in our 3 digit multiplier to get 625. Now all we have to do is 1001 x 625 which is 625625.
This puzzle was on TED-Ed. If you're curious, it's the "chests of pearls" riddle (look up "ted-ed sea monsters riddle").
Good ol' 1001, but let's say we don't know that 1001 magic. Now since the number N ends in 5 it will be divisible by 7x11x13x5 = 5005. To go from 5005 to a six digit number starting with 6 we need to multiply by 12Y where Y has to be odd, so N will end in 5 (for y = even N would end in 0). 121 and 123 won't do it, so it's 125: 5005x125= 625625
Nice!
Sorry I'm still having trouble understanding it. Would anyone explain it baby terms?
If a number is to be completely divisible by 7, 11 and 13 and is a 6 digit number, it is also going to be divisible by 7x11x13 which is 1001. From here you don't need to follow his method if you don't want to. Even without knowing the property of a 6 digit number multiplied by 1001 having repetitive digits, you can just try to guess it with the first 2 digits and the last digit. The last digit is 5 so 1001 is multiplied with a number that ends with 5. Also, the first digit of that number also needs to be 6 for the first digit of the unknown number's first digit to be 6. And since 1001 has 4 digits and the unknown number has 6 digits, we know that 1001 is multiplied with a 3 digit number. So we are looking at a 3 digit number that starts with 6 and ends with 5. Since second digit is 2 of the unknown number is 2, we just try 2 in our 3 digit multiplier to get 625. Now all we have to do is 1001 x 625 which is 625625.