They all fall in the middle. 15 February was the middle of February (1984 being a leap year). 2 July was the middle day of the year 1983. And 16 December was the middle of December.
What is it that speaks without any words? And can be loudly and distinctly heard? Will drive away friend, and foe alike. And is enough to make a stolid man’s face alight?
When Florence and Willie finished playing darts, they proudly announced that their 3-digit scores added up to exactly 800 points. Furthermore, each of their scores shared the same 3 digits, without any repeating digits.
You could figure this out mathematically, but instead, I plugged in digits that added up to 10 for the first column, 9 for the second column (since you carry the 1) and 7 for the third column (again, because you’re carrying the 1).
Pawns in a chess game. There are eight pawns and they are only permitted to move forward, not backward and the primary objective in chess is to protect the king.
There are two tricks to this one. The first is 1 × 0. But it’s mostly there as a distraction. Yes, 1 × 0 is 0, but that doesn’t affect anything else in the equation. The second, far trickier element is that the lines ending with 1 don’t have a + sign next to them. That means they should be combined with the following line.
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.