### Brain Teasers

# Gifting Away !

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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