Question 1209737: The dots on the opposite faces of a die have a sum of 7. How many different sum of dots on three adjacent faces are there on a die?
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to figure out the different possible sums of dots on three adjacent faces of a standard die:
1. **Visualize:** Imagine a die. Three adjacent faces share a common vertex (corner).
2. **Consider the possibilities:** Since opposite faces sum to 7, the possible sets of three faces sharing a vertex are limited. Let's represent the faces by the number of dots on them.
3. **List the combinations:** We can't have opposite faces together. Here are the distinct sets of three adjacent faces and their sums:
* {1, 2, 3}: Sum = 6
* {1, 2, 4}: Sum = 7
* {1, 2, 5}: Sum = 8
* {1, 2, 6}: Sum = 9
* {1, 3, 4}: Sum = 8
* {1, 3, 5}: Sum = 9
* {1, 3, 6}: Sum = 10
* {1, 4, 5}: Sum = 10
* {1, 4, 6}: Sum = 11
* {1, 5, 6}: Sum = 12
* {2, 3, 4}: Sum = 9
* {2, 3, 5}: Sum = 10
* {2, 3, 6}: Sum = 11
* {2, 4, 5}: Sum = 11
* {2, 4, 6}: Sum = 12
* {2, 5, 6}: Sum = 13
* {3, 4, 5}: Sum = 12
* {3, 4, 6}: Sum = 13
* {3, 5, 6}: Sum = 14
* {4, 5, 6}: Sum = 15
4. **Identify the unique sums:** The unique sums we found are 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15.
5. **Count:** There are 10 different possible sums.
Therefore, there are 10 different sums of dots on three adjacent faces of a die.
Answer by ikleyn(52747)  (Show Source):
You can put this solution on YOUR website! .
In his post, @CPhill gives this answer:
* * * There are 10 different sums of dots on three adjacent faces of a die. * * *
This answer is INCORRECT and, even more, is IRRELEVANT to the problem.
I will easily disprove it.
Indeed, a die has 8 corners, in all, so the number of different sums
under the problem's question can not be more than 8.
Ha - ha - ha.
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Regarding the post by @CPhill . . .
Keep in mind that @CPhill is a pseudonym for the Google artificial intelligence.
The artificial intelligence is like a baby now. It is in the experimental stage
of development and can make mistakes and produce nonsense without any embarrassment.
It has no feeling of shame - it is shameless.
This time, again, it made an error.
Although the @CPhill' solutions are copy-paste Google AI solutions, there is one essential difference.
Every time, Google AI makes a note at the end of its solutions that Google AI is experimental
and can make errors/mistakes.
All @CPhill' solutions are copy-paste of Google AI solutions, with one difference:
@PChill never makes this notice and never says that his solutions are copy-past that of Google.
So, he NEVER SAYS TRUTH.
Every time, @CPhill embarrassed to tell the truth.
But I am not embarrassing to tell the truth, as it is my duty at this forum.
And the last my comment.
When you obtain such posts from @CPhill, remember, that NOBODY is responsible for their correctness,
until the specialists and experts will check and confirm their correctness.
Without it, their reliability is ZERO and their creadability is ZERO, too.
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