John has eleven friends. He has a bowl containing eleven apples. Now He wants to divide the eleven apples among his friends, in such a way that an apple should remain in his bowl.
How can He do it?
If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.
A small town is visited by an ice-cream truck every day. On the first day of February, the truck visits as usual and 5 children, one from each of the first 5 houses on the street buys an ice cream that is of the different flavor from each other along with a completely different topping.
Go through the details below and find out which child lives in which house and bought which ice-cream flavor with which topping:
1. Jim lives between the child who bought the Raspberry topping and the child who bought mango ice cream.
2. Joyce, whose house has an even number, bought the cherry topping. Nancy does not live next to Joyce.
3. The blackcurrant ice cream had no topping.
4. The child who lives in house number 2 had the butterscotch ice cream. The child in house number 3 did not have chocolate ice cream.
5. Mike had banana ice cream. He hates banana cherry.
6. The child who had the cashew topping lives in house number 5. Dustin does not live in house number 4.
Please note that the odd numbered houses and the even numbered houses are located on the exactly opposite sides of the street.
You are given a set of weighing scales and 12 marbles. The scales are of the old balance variety. That is, a small dish hangs from each end of a rod that is balanced in the middle. The device enables you to conclude either that the contents of the dishes weigh the same or that the dish that falls lower has heavier contents than the other. The 12 marbles appear to be identical. 11 of them are identical, and one is of a different weight. Your task is to identify the unusual marble and discard it. You are allowed to use the scales three times if you wish, but no more. Note that the unusual marble may be heavier or lighter than the others. You are asked to both identify it and determine whether it is heavy or light
