Lesson Logic problems - The solution to Problem 3

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The solution to Problem 3


Below  (after the  reminder)  is the  solution  to the  Problem 3  of the lesson  Some logic problems  (the topic  Miscellaneous word problems
of the section  Word problems  in this site).
Problem 3 formulation (reminder)
Seven dwarfs decided that each of them will give a gift of at least  7  flowers to Snow White for her birthday.
When all the flowers were presented,  Snow White said that the total number of the flowers is not more than  50.
When the smallest dwarf heard it,  he said immediately that he can identify exactly the number of flowers presented by each dwarf.
What is the number of flowers presented by each dwarf?

Solution
It follows from the problem statement that there are two major opportunities:
    1)  each dwarf gave a gift of  7  flowers,  totally  49  flowers,  and
    2)  one of dwarfs gave a gift of  8  flowers,  while six others dwarfs gave  7  flowers each,  totally  6*7+8 = 42+8 = 50  flowers.

If it was the smallest dwarf who gave a gift of  8  flowers,  then the only one option exists:  each of the rest six dwarfs gave  7  flowers.
Therefore,  in this case the smallest dwarf is in position to make his suggestion.

If,  in opposite,  the smallest dwarf gave a gift of  7  flowers,  then two options exist:
    a)  each of the rest six dwarfs gave a gift of  7  flowers,  and
    b)  one of the rest six dwarfs gave  8  flowers,  while five others gave  7  flowers each.

In this case the smallest dwarf does not know,  which one of these two options is in the place,  so he can not make his suggestion.

Thus,  if the smallest dwarf gave a gift of  8  flowers,  he can make his suggestion;  this suggestion is right,  and this is the only
case when the smallest dwarf can make such a suggestion.

Based in this,  we can conclude that the smallest dwarf gave a gift of  8  flowers,  and the rest of six dwarfs
gave a gift of  7  flowers each.

Answer
The smallest dwarf gave a gift of  8  flowers.
The rest of six dwarfs gave a gift of  7  flowers each.

Back to the original lesson  Some logic problems  (the topic  Miscellaneous word problems  of the section  Word problems  in this site).

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