Alfred and Bill are clerks at the local grocery store. Alfred can stock a shelf in 20 minutes, but Bill is new and takes 30 minutes. How long would it take for them to stock a shelf together?
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.
1. Each letter represents a different digit from 1 to 9 2. The total of each row is 17. 3. (B × B) + B + F = A 4. C × F = EF (a 2-digit number, not their product)
A + B + C = 17 D + E + F = 17 B2 + B + F = A C × F = EF
To begin with, B has to be a 1 or 2 or else A wouldn’t be a single digit. Plug in B = 2, gives you 6 + F = A, meaning F and A can only be (1,7) or (3,9). To get 17, C would have to be 8 or 6, but those values don’t work for C × F = EF. So B must be 1.
2 + F = A means F and A can be (2,4), (3,5), (4,6), (5,7), (6,8) or (7,9). To get 17 on the top row, the only option that leaves C as a single digit is F = 5 and A = 7.
C × F = EF 9 × 5 = 45, so E = 4 and D = 8 to make the second row equal to 17.
Evianna meets a man while attending her mother’s funeral. She becomes infatuated with him and he reciprocates the interest, but he leaves the funeral without giving her any contact information. She tries to locate him but is unsuccessful. Several days later she kills her sister.
Because she’s a psychopath. She killed her sister because she hoped the man would attend the funeral and she would get to see him again. This is one brain teaser that is probably best that you don’t get the correct answer. If you knew the answer right away and thought it was obvious, you may want to talk to someone.
The word vex. “v” is Roman numeral 5, which is odd. “x” is Roman numeral 10, which is even. “e” is the base of the natural logarithm and is irrational (e = 2.718281828…). Its mantissa (the part to the right of the decimal point) is infinitely long.