## Fire Island (SPRING 2016)

### Puzzle:

A man is stranded on an island covered in forest.

One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.

How can the man survive the fire? There are cliffs around the island, so he cannot jump off, and there are no buckets or any other means to put out the fire

### Solution:

The man picks up a piece of wood and lights it from the fire on the west end of the island.

He then quickly carries it near the east end of he island and starts a new fire. The wind will cause that fire to burn out the eastern end and he can then shelter in the burnt area.

The man survives the fire, but dies of starvation, with all the food in the forest burnt.

(SOURCE: Math Is Fun)

## Absolutely Christmas Crackers (SUMMER 2016)

### Puzzle:

I’ve sent off for one of those kits that you can use to make your own Christmas crackers, which are given as small tokens during the holidays. The kit contains:

• Three colors for paper hats: red, yellow, and blue
• Four types of novelty items: a toy car, spinning top, magnifying glass, and miniature hair brush
• Four different jokes written on slips of paper

All the other parts are the same type. The kit contains enough parts for 50 crackers.

Can I make each cracker different from all the others?

### Solution:

3 x 4 x 4 = 48. Sadly at least two crackers must be exact duplicates of ones already made. BUT if you could handle the sad look on people's faces, you could consider a missing item as a possible combination. This gives 4 x 5 x 5 = 100 different crackers. 40 crackers would be missing one item, 11 will be missing two, and one cracker would be missing nothing at all!

(SOURCE: Math Is Fun)

## A Question of Time (FALL 2016)

### Puzzle:

If the hour and minute hands are at equal distance from the 6 hour, what time will it be exactly?

### Solution:

Say the answer is “8 hours X minutes." According to proposition, the angle between the minute hand and the "mark 4" of the watch is equal to the angle between the hour hand and the "mark 8" of the watch.

We know that the minute hand makes 360 degrees (360/60=6 degrees per minute) in 60 minutes, and the hour hand makes 360/12=30 degrees (30/60=1/2 degrees per minute) in the same time.

Therefore, (20-X) minutes correspond to 6(20-X) degrees (this is the angle between the minute hand and the "mark 4"). And in X minutes, the hour hand makes X/2 degrees with the "mark 8".

Thus, X/2=6 * (20-X) gives X=18 minutes 27 and 9/13 second. So, the answer is 8 hours, 18 minutes, 27 9/13 second.

(SOURCE: Math Is Fun)

## Old Masters (WINTER 2016)

### Puzzle:

Three friends —Pablo, Edvard, and Henri— are talking to each other about the art collection of a mutual acquaintance, Leonardo. Pablo says, “Leonardo has at least four paintings of Rembrandt.” Edvard says, “No, he has less than four paintings of Rembrandt.” “According me,” says Henri, “Leonardo has at least one Rembrandt.” If you know that only one of the three friends is right, then how many Rembrandts does Leonardo possesses?

### Solution:

Look at the statements about the number of paintings of Rembrandt. If Pablo would be right ("at least four"), then Henri ("at least one") would also be right. If Henri would be right ("at least one"), then or Pablo ("at least four") or Edvard ("less than four") would also be right. This means only Edvard can be right and Leonardo possesses less than one Rembrandt, so no Rembrandt at all.