Gifting Away !
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.
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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