Is it unique 3?
A strictly increasing number is a number whose digits are increasing from left to right (for example 145, 3689 are such numbers, while 108 and 3557 are not).
Find the 3-digit strictly increasing number , such that is also strictly increasing.
For more problems like this, try answering this set .
The answer is 578.
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1 solution
First we observe that 6n is a 4-digit number (which you can easily prove since if that was not the case, 6n could only be 678, which means that n = 113, which is not strictly increasing). Now, we have to find the last digit of n (call it x). The last digit of 6n will always be greater than 4, (because the smallest possible strictly increasing 4-digit number is 1234, which is not divisible by 3, and therefore not by 6). That means that the last digit of 6x is greater than 4, and that x > 4. The only two possible solutions for x are 6 and 8. Choose 6. Now, we have to find the middle digit of n (call it y). The last digit of 6y should be smaller than 3 (if it isn't, then the third digit of 6n is greater or equal to the last, which is 6). That means y can only be 2, and that the first digit of n (call it z) must be 1, which is a contradiction considering 6 * 126 is a 3-digit number (and is not a strictly increasing number, of course). We obviously have to choose 8 as x. Then, we choose such y that the last digit of 6y is smaller than 4, so we have two possibilities: 2 and 7. Because we want 6n to be a 4-digit number, we choose 7 as y. From here, it's obvious that z = 5. n = 578