I hesitated to add this because it’s poorly worded, ambiguous and the answer could be almost anything. I prefer teasers with a single answer, but there you go.
If you came up with a different answer and can explain how you did it, don’t think you’re wrong. It’s probably just as valid. Feel free to share yours in the comments.
My answer for the first number is 2.
Here’s how I got it.
The generic rule for a number in the sequence is: 2^(n – 1) + 1, where n is the position in the sequence.
Note: The teaser doesn’t specify the position of 17. In this case, it’s fifth.
Position 1: (so n = 1) is 2^(1 – 1) + 1 = 2
Position 2: 2^(2 – 1) + 1 = 3
Position 3: 2^(3 – 1) + 1 = 5
Position 4: 2^(4 – 1) + 1 = 9
Position 5: 2^(5 – 1) + 1 = 17
For the curious, the next 5 numbers of the sequence would be:
Priscilla gave her brother Bruce as much money as Bruce started with. Bruce gave Priscilla as much money as Priscilla had left. Priscilla then gave Bruce as much as Bruce had left, which left Priscilla broke. Bruce had $80.00.
How much money did Priscilla and Bruce start with?
A princess is as old as the prince will be when the princess is twice the age that the prince was when the princess’s age was half the sum of their present ages.
This one took a while to figure out and there are numerous valid ways of finding the answer.
Here is the solution I came up with
I created the following table from the riddle:
Current
Future
Past
Princess
x
2z
(x+y)/2
Prince
y
x
z
I then created three equations, since the difference in their age will always be the same. d = the difference in ages x – y = d 2z – x = d x/2 + y/2 – z = d
I then created a matrix and solved it using row reduction.
x
y
z
1
-1
0
d
-1
0
2
d
.5
.5
-1
d
It reduced to:
x
y
z
1
0
0
4d
0
1
0
3d
0
0
1
5d/2
This means that you can pick any difference you want (an even one presumably because you want integer ages). Princess age: 4d Prince age: 3d
Ages that work
Princess
Prince
4
3
8
6
16
12
24
18
32
24
40
30
48
36
56
42
64
48
72
54
80
60
To see other solutions check out the comments from when I posted this on my blog.
Twenty one points divide and dance, Twirling and leaping about, Ladies, Romans and knights of France, Craving a victor’s rout, Wrought of wood, ivory or bone, An exciting yet vicious pursuit, Ancient, forbidden and crooked, All in search of the loot.
A die. The standard die has 21 pips (or points), divided up on the six sides of the die which dance around when rolled. Ladies, knights and Romans all played dice as a pastime (though not together). Dice can be made of wood, ivory and bone, among other materials. Dice have been used in Asia since before recorded history and many governments tried unsuccessfully to outlaw the game. Professional gamblers were common and often used loaded dice. Desperate German chaps even bet their own liberty on a single roll of the dice.
If a cork is placed into a glass of water, it will almost always drift to the side of the glass. There is one simple way, however, to get the cork to float in the center of the glass. What is it?
Water, the glass, and the cork are all that is required.
The reason that a cork drifts to the side of a glass is that it floats to the highest point. Since water “clings” to the glass, the highest point is around the edge of the water. To get the cork to float in the middle of the glass, all you have to do is fill the glass as much as possible. The water will form a convex shape above the glass, with the highest point at its center. This is where the cork will settle.
I’m up and down and round about, yet all the world can’t find me out. Though thousands have employed their leisure, they never yet could find my measure. I’m found in almost every garden, In a compass or a farden. There’s neither chariot coach nor mill may move one inch except I will.