Discussion Overview
The discussion revolves around calculating the number of 5-digit numbers that can be formed using specific digits and are divisible by 8. The two scenarios considered are: one where repetition of digits is not allowed (using the digits 1, 2, 3, 4, 5) and another where repetition is allowed (using the digits 0, 1, 2, 3, 4, 5).
Discussion Character
- Mathematical reasoning, Debate/contested
Main Points Raised
- Some participants propose that for 5-digit numbers formed from the digits {1, 2, 3, 4, 5} and divisible by 8 (without repetition), the valid endings are limited, leading to a calculation of 10 such numbers.
- Others argue that for 5-digit numbers formed from the digits {0, 1, 2, 3, 4, 5} and divisible by 8 (with repetition allowed), additional valid endings increase the total to 185, based on the combinations of digits.
- A later reply questions the complexity introduced by the inclusion of the digit 0 in the second scenario, suggesting that the number of valid endings is greater than initially considered, with a calculation yielding 24 possible endings based on even and odd digit placements.
- One participant acknowledges a mistake regarding the consideration of the digit 0 in their previous calculations.
Areas of Agreement / Disagreement
Participants generally agree on the approach for the first scenario but express differing views on the second scenario, particularly regarding the impact of including the digit 0 and the resulting calculations. The discussion remains unresolved with multiple competing views on the second part.
Contextual Notes
There are unresolved assumptions regarding the specific combinations of digits and the conditions for divisibility by 8, particularly in the second scenario where the presence of 0 complicates the calculations.