self Maths Puzzle

You have a basket containing ten apples. You have ten friends, who each desire an apple. You give each of your friends one apple.

After a few minutes each of your friends has one apple each, yet there is an apple remaining in the basket.

How?

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self Other Question

This is a simple Number System Problem, posted under Placement Category

Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?

1)(x-z)2 y is even 2)(x-z)y2 is odd 3) (x-z)y is odd 4)(x-y)2z is even
At the Party:
1. There were 9 men and children.
2. There were 2 more women than children.
3. The number of different man-woman couples possible was 24. Note that if
there were 7 men and 5 women, then there would have been 35 manwoman
couples possible.
Also, of the three groups - men, women and children - at the party:
4. There were 4 of one group.
5. There were 6 of one group.
6. There were 8 of one group.
Exactly one of the above 6 statements is false.
Can you tell which one is false? Also, how many men, women and children are
there at the party?