BMAD

This is a modified version of the famous light-bulb problem.  

There are three switches in the hallway.  turning on the switches in different combinations cause different light-bulbs in the room to turn on. There are six light-bulbs and from turning on all of the possible combinations, each light-bulb is turned on at most twice (in other words there are only two ways to turn on a light-bulb).  We need to map the switches to the light-bulbs.  

The only things we know is that flicking 1 switch causes 1 light-bulb to turn-on, flicking 2 switches causes 2 to turn-on, and flicking all 3 cause three light-bulbs to turn-on and if a switch turns on a light-bulb, that switch must be on to turn it on again (even if flicking 2 switches).

What is the fewest number of 'tests' needed to effectively map the light-bulbs to the switches?

How much does the baby weigh if the mother weighs 100 pounds more than the combined weight of the baby and the dog, and the dog weighs 60 percent less than the baby?

 weigh-the-baby.jpg   11.72KB   9 downloads

The Basics of Modified Deal or No Deal:

There are ten boxes labeled 1 through 10.

The boxes have a check in them worth from .01 to 10,000,000 dollars as such $.01, $.10, $1.00, $10.00, $100.00, $1000.00, $10,000, $100,000, $1,000,000, and $10,000,000).  

The amounts are randomly placed in the marked boxes.

The player first selects their chosen box.

The game proceeds as folllows:

Round 1:

The player select 2 boxes to be revealed

--An offer is made to the player, if the player agrees, the game is over.

Round 2:

if not- the player selects 2 boxes to be revealed

--An offer is made to the player, if the player agrees, the game is over.

Round 3:

if not- the player selects 2 boxes to be revealed

--An offer is made to the player, if the player selects, the game is over.

Round 4:

if not- the player selects 2 boxes to be revealed

--An offer is made to the player, if the player selects, the game is over.

Round 5:

if not- the player's chosen box is revealed and they take the prize.

The individual making the offer to the player is known as the banker.  It is well-known, in this game, that the banker offers 85% below the median of the boxes for the first round and increases that percentage by 5% of the median of the remaining boxes each later round.  A player was made the following offers

Round 1: 4,675.00

Round 2: 4,950.00

Round 3: 5,225.00

Round 4: 5,500.00

What boxes were chosen each round?

Should the player take the offer?

three towns are located such that they are equal distant to the center of a park.  What is longer, walking from one city to the other two or walking to the park and back?

note: by taking straight paths