### Brain Teasers

# Gifting Away !

Logic
Logic puzzles require you to think. You will have to be logical in your reasoning.

Five gift boxes have to be prepared to be given to five of my nephews. I have 5 cakes, 6 toffees, 4 pastries and 3 toys. Each of the boxes should contain at least one cake, at least one toffee, at least 3 items and at the most 4 items. Pastry and toy cannot be in the same box. No box can contain two toys.

Which of the following must be true?

1) Exactly one box should contain 2 toffees and 1 toy.

2) Exactly one box should contain 2 toffees.

3) Exactly one box should contain 2 pastries.

NOTE: Out of the given set of 3 statements, it is not necessary that one and only one statement is true. One or more statements may be true.

Which of the following must be true?

1) Exactly one box should contain 2 toffees and 1 toy.

2) Exactly one box should contain 2 toffees.

3) Exactly one box should contain 2 pastries.

NOTE: Out of the given set of 3 statements, it is not necessary that one and only one statement is true. One or more statements may be true.

### Answer

Statements 1 and 2 are true.The given statements are

1) Exactly one box should contain 2 toffees and 1 toy.

2) Exactly one box should contain 2 toffees.

3) Exactly one box should contain 2 pastries.

Also the given observations are

A) Each of the box should contain at least one cake, at least one toffee, at least 3 items and at the most 4 items.

B) Pastry and toy cannot be in the same box.

C) No box can contain two toys.

Using observations A and C, the following is the definite distribution to be made :-

Boxes 1 2 3 4 5

Cake 1 1 1 1 1

Toffee 1 1 1 1 1

Pastry

Toy 1 1 1

since the cakes and toffees must follow observation A of at least 1 in each of the boxes and toys must follow observation C of no more than one toy in a box.

We have 4 pastries and 1 toffee remaining to be distributed to these 5 boxes.

From observation B, since pastry and toy cannot be in the same box, the 4 pastries must go to boxes 4 and 5. Also in order to keep with the later part of observation A of at least 3 items and at most 4 items, these four pastries must be packed 2 each into boxes 4 and 5.

The remaining toffee must go into one of the three boxes 1, 2 or 3. Let us assume that this toffee goes to box 1.

Hence the final distribution is as follows :-

Boxes 1 2 3 4 5

Cake 1 1 1 1 1

Toffee 2 1 1 1 1

Pastry 2 2

Toy 1 1 1

Comparing the given statements with the above distribution we can see that statements 1 and 2 are true since they refer to box 1 and statement 3 is false because more than one box is available with two pastries.

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