### Brain Teasers

# Buying Steaks

You are buying steaks at a butcher's. You see that he has 12 steaks: six worth $4 each and six worth $6 each. The butcher tells you, however, that if you let him pick the steaks he will charge you $4 apiece and if you pick the steaks he will charge you $6 apiece, no matter which steaks are chosen. What should you do to get the best deal?

Assume that the actual number of steaks you purchase is of no concern, except for the butcher's deal. In other words you'd be just as happy buying 5 steaks as you would buying no steaks.

Assume that the actual number of steaks you purchase is of no concern, except for the butcher's deal. In other words you'd be just as happy buying 5 steaks as you would buying no steaks.

### Answer

You should ask the butcher to give you eleven steaks, and let him choose.If you choose the steaks, you will obviously pay the maximum price possible ($6 each), no matter how many steaks you buy.

If you let the butcher choose, he will pick the six $4 steaks first, so the only way you can make him give you some $6 steaks is to order more than six. Ordering all twelve would mean that you paid $4 per steak, averaging $5 each in value. You saved $1 per steak.

However, if you order all 12 then you are technically choosing the steaks (because saying "give me all of them" is just a shorter way of saying "give me that one, and that one, and..."), so you would have to ask for 11 and let the butcher pick them at his discretion.

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