In 2014, Howard returned from his football game later than normal and Trudy, his Mom, was concerned. She asked what position he played, and he said he was a lineman. She asked what team they played and he said the Bears. She asked if anything strange had happened, and he said no. She asked what the score was and he said their team won, 14-1. Satisfied, Trudy sent Howard up to bed. The next morning Trudy told her husband Mick about her conversation with Howard. Mick’s face turned red and he stormed up to Howard’s room.
Mick knew Howard was lying about being at the football game because in American football it’s impossible to score just 1 point (before the 2015 one-point safety rule). A score of 2 is the lowest possible score (awarded for a safety). In fact, 1 is the only impossible score in football. You can score 2 points for a safety, 3 points for a field goal and 6 points for a touchdown, with an extra point for the field goal. You also have the option to go for another touchdown for a 2-point conversion. With 2, 3, 6 and 7 you can generate any other number except for 1.
For example, here are ways a team could score from 2 to 10 points. 2 = safety 3 = field goal 4 = 2 + 2 5 = 3 + 2 6 = touchdown 7 = touchdown and extra point attempt 8 = touchdown and two point conversion 9 = touchdown and field goal 10 = touchdown, extra point attempt and field goal
I am the owner of a pet store. If I put in one canary per cage, I have one bird too many. If I put in two canaries per cage, I have one cage too many. How many cages and canaries do I have?
If you put one canary in each cage, you have an extra bird without a cage. However, if you put two canaries in each cage then you have two canaries in the first cage, two canaries in the second cage and an extra cage.
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.
