SUPER SALE PUZZLE

A TV Game show SUPER SALE had a winner who was a businessman. To earn the final gift he has to apply his arithmatic and business skills. The gift is in the form of a puzzle.

He will be given 100$ and allowed to shop in a Mall and buy several pairs of gloves and slippers from 2 neighboring shops.


Shop #1 has a pair of gloves for 15$ and a pair of slippers for 5$. Whereas the neighboring shop #2 has similar gloves for about 10$ and a pair of slippers for 8$.

1. The man can buy from both the shops but has to start from Shop #1.

2. The man can return goods to a shop. But the money back policy say that he can only do that if the items are purchased from the same Shop.

3. When returned, Shopkeeper #1 will cut a tax of 10% on the total cost of the goods calculated with the item price applicable in Shop #1. Similarly Shopkeeper #2 will cut a tax of 15% on the total purchased cost of the goods returned to Shop #2.

So if the man returns a pair of gloves (originally purchased from Shop #2) to Shop #2 back, he will be given 10 - (10 * 15/100) = 10 - 1.5 = 8.5 $ back.

4. The man cannot return goods to a shop if they are originally purchased from the other shop. But instead, he can participate in Exchange Scheme as follows...

5. In Exchange Scheme, the man will earn following discounts same in both shops.

i. An old pair of gloves will earn 60% OFF on a new pair of gloves
(so exchange price of gloves in Shop #1 will be = 15 - (15 * 60/100) = 6)

ii. An old pair of slippers we will earn 50% OFF on a new pair of slippers
(so exchange price of slippers in Shop #2 will be = 8 - (8 * 50/100) = 4)

The man can exchange items irrespective of the shop they are purchased from. But why to perform an exchange of goods with the same shop where you can return them under the money back policy (Point 3). Why to indulge into a less profitable exchange offer with same shop. Correct!

6. Now comes the interesting SUPER SALE Offer says that if the man purchases 5 pairs of gloves from a shop, it will earn him 2 pairs of slippers FREE. Similarly a pair gloves are FREE on purchase of 4 pairs of slippers.

FREEly earned items cannot be returned but only exchanged. So you can exchange them with same shop they are purchased from (Thank God! )

7. If a shop sells everything and is void of an item then it will not participate in any further transaction of that particular good i.e. if Shop #2 sells all its gloves then it would not be able to Give (Sale or Offer FREE) or even Take (Buy or Exchange) any more gloves from the man.

8. Both shops have 20 pairs of gloves and 20 pairs of slippers each.

9. The man can perform maximum of 5 transactions (give or take) with each shop.


After final purchase, price money equivalent to the orginal market price of the items i.e. a pair of gloves = 15$ and a pair of slippers = 8$ will be given to the man for each pair of items he had purchased within above 9 criteria on the SUPER SALE..

So the question is ....
How much maximum price money can the man earn in the above SALE? Can he earn any profit on the first place?

Frankly I am bad at drafting this solution on paper So I am writing a Java program to calculate for this scenario. Meanwhile if you guys can answer or hint me about this I would be greatly helped.

I was told, although, that there can be multiple solutions as far as the number of pairs of gloves & slippers are concerned .... the maximum profit money earned is a unique figure.

ALL THE BEST!