WG declared as follows:
My number
1. Comprises 7 digits.
2. Uses only 3 distinct digits.
3. Is a square.
4. Is a cube.
5. Is somewhere between 4,500,000 and 8,500,000.
6. Sum of its digits is 45.

One (and only one) of the above statements is false.
Erase it and recover the number.
Is it possible to ignore additional statement(s) and still stay with the original number?

The false statement is 3.

The number 7077888
  (1) comprises of 7 digits,
  (2) uses only 3 distinct digits {0,7,8},
  (4) is a cube {192^3}
  (5) is >= 4,500,000 and <= 8,500,000
  (6) has SOD = 45 {7+0+7+7+8+8+8 = 45}

Yes. As statement #5 is a subset of statement #1, and is one of the true statements, statement #1 does not need be stated to determine the original number. With statement #2 retained, statement #6 may also be omitted; in addition, if both statements #1 and #2 are retained, statement #5 is unnecessary and could be erased.

Edited on September 4, 2020, 9:51 am

Posted by Dej Mar on 2020-09-04 09:00:14