Sunday Morning Puzzle # 11

Kings may select advisors based on esoteric hat color divination rituals, but Generals are more practical. Generals look for brains and courage. The General’s advisor makes the big bucks, drives the big car, lives in the big house and has first pick of any of the maidens in the land. Due to an unfortunate incident on the front lines, that job is now open.

“Brains and courage”, you think. “Sounds like my kind of job.” You apply.

But maybe you should re-consider. The General has a pretty tough system for weeding out the wannabes. The candidate is allowed to choose a weapon, and then lowered into a pit. Waiting out of sight at the bottom of the deep pit are 4 gigantic genetically engineered poisonous snakes–either cobras or kraits.

Here are the choice of weapons:

Weapon #1: Kills as many kraits as desired, but can only kill 1 cobra.
Weapon #2*: Kills exactly 2 cobras, and exactly 2 kraits. Weapon #2 cannot kill more than 2 of either kind of snake.
Weapon #3: Kills as many cobras as desired, but can only kill 1 krait.

*****It should be noted (but this is probably irrelevant) that Weapon #2 fails about 1 in 10,000 times.

If your weapon does not match the snake quantities in the pit…well… R.I.P.


scenario A

The General will secretly place 4 snakes in the pit prior to the test. You will not have the opportunity to look in the pit before choosing your weapon. Here is the method the General uses to select snakes:

The General flips a fair coin (a quarter, to be precise). If it is heads, he puts in a cobra. If tails, he puts in a krait. This process is repeated until there are 4 snakes in the pit.

You also learn this: During the genetic engineering process, all the cobras have become “singing cobras”. If anyone begins humming a tune around any of these cobras, then the 2 largest of the cobras will begin to sing along to the music. Only the 2 largest cobras will sing, though. Any other cobras will remain quiet. Cobras like to sing, but they believe that 2 singing snakes are enough.

Kraits never sing.

So the test begins. You are led blindfolded to the side of the pit. Your blindfold is removed. You are told to select a weapon. Quickly you begin loudly humming the first song that pops into your head. It’s Jim Stafford’s old classic: “Spiders and Snakes”.

As you hum you hear a sound coming from the pit. It is the sound of 2 snakes singing:

“I don’t like ssspiders and sssnakes, but that ain’t what it takesss to love me…”

Question #1: Which weapon do you select to give you the highest probability of defeating the snakes?


**scenario B **

Same as above with these exceptions:

  1. Now there are some whistling kraits. All whistling kraits whistle along to any music being sung.
  2. The General still flips a quarter and puts a cobra in the pit if it comes up heads. However, should the quarter come up tails the General then flips a dime. If the dime comes up heads he puts a whistling krait in the pit. If it comes up tails he puts a regular old quiet krait in the pit.
    This whole quarter-dime process is repeated until there are 4 snakes in the pit–either singing cobras, whistling kraits, quiet kraits, or some combination of these.
  3. When you approach the pit and begin humming, you not only hear two snakes singing, but you also hear exactly 1 snake whistling.

Question #2: Now which weapon do you choose?


Question #3: Which of the above two scenarios gives you the best chance of emerging victorious?

Question 1. The remaining possibilities are:
two cobras (25% chance on the coin flips)
one cobra, one krait (50% chance)
two kraits (25% chance)

Weapon 3 gives me a seventy five percent change of surviving.

Question 2.

There are at least two cobras and one krait, the remaining possiblities:

one cobra (50% chance on the coin flip)
one non-singing krait (25% on the coin flip)

So I would take the Weapon 3 again.

But I feel better about scenario 1.

Please proceed to correct me at your leisure.

Well, Uncle Bill sure has this thread by the short hairs.

Scenario A: There are either 2, 3, or 4 cobras in the pit, the possibilites occuring in the ratio 6, 4, 1 respectively.

Your chance of surviving: with W1 = 0, with W2 = 6/11 = 54.55%, with W3 = 5/11 = 45.45 %.

Scenario B: Since there is only 1 whistler and at least 2 cobras, the possibilities are 2C1W1Q or 3C1W0Q. These occur in the ratio of 12 to 8.

Your chance here: with W1 = 0, with W2 = 12/20 = 60%, with W3 = 8/20 = 40 %.

So I’m picking W2 all day. The failure rate you suggest for W2 is not large enough to cause one to change to W3, although if I succumbed to possibly multiple venomous serpent bites because of manufacturor error I would be royally pissed.

Congrats to the NEW advisor to the General: jcgmoi!
Good luck with all the money, the house, and the maidens. Stay away from the front lines.