Question

there are only two numbers with the property that every digit except zero appears just once in the number and its square.one of these numbers is 854, since 854*854= 729316. the other number is made up of three consecutive digits in increasing order.what is the other number?

Answer 1

To find the other number, let's consider the properties mentioned:

1) Every digit except zero appears just once in the number
2) The number and its square have this property

First, we can list all the numbers with three consecutive digits in increasing order: 123, 234, 345, 456, 567, 678, 789.

Next, we can square these numbers to see if they satisfy property 1:

- 123*123 = 15129 (Missing 4, 6, 8)
- 234*234 = 54756 (Missing 1, 8, 9)
- 345*345 = 119025 (Missing 6, 7, 8)
- 456*456 = 207936 (Missing 1, 2, 5 and 7)
- 567*567 = 321489 (Missing 0, 2, 6)
- 678*678 = 459684 (Missing 1, 2, 3 and 9)
- 789*789 = 622521 (Missing 0, 3, 4 and 6)

Out of all of these, the only number that satisfies property 1 is 345. Therefore, the other number with the given properties is 345.