So way back a long time ago (I don’t even remember when) I bought a bunch of random math & physics problem books. It must have been when I wanted to be a physics god so late high school or early college.
Anyways. One of the books I got is called “The Moscow Puzzles” by Boris Kordemsky. Supposedly (from the book’s introduction) this was the most popular mathematics puzzle book ever published in the Soviet Union.
I went through a few of the problems today, and I think I’ll make this a daily, or at least almost daily thing. After doing a couple I figured maybe it’d be a fun thing to share here. So each post will just have whatever problems I went through for the day with the solutions.
Chapter 1 – “Amusing Problems”
The intro for chapter 1 says this:
To see how good your brain is, let’s first put it to work on problems that require only perseverance, patience, sharpness of mind, and the ability to add, subtract, multiply, and divide whole numbers.
1. Observant Children
A schoolboy and a schoolgirl have just completed some meteorological measurements. They are resting on a knoll. A freight train is passing, its locomotive fiercely fuming and huffing as it pulls the train up a slight incline. Along the railroad bed the wind is wafting evenly, without gusts.
“What wind speed did our measurements show?” the boy asked.
“Twenty miles per hour.”
“That is enough to tell me the train’s speed.”
“Well now.” The girl was dubious.
“All you have to do is watch the movement of the train a bit more closely.”
The girl thought awhile an also figured it out.
What was the train’s speed?
The speed is 20 mph. The only way you’d be able to tell the speed of the train is by observing the smoke coming out of it. If the smoke appears to be going straight up, you’d know it is going the same speed as the wind.
3. Moving Checkers
Place 6 checkers on a table in a row, alternating them black, white, black, white, black, white. (Here, X = black, O = white)
[ ] [ ] [ ] [ ] [X] [O] [X] [O] [X] [O]
Leave a vacant place large enough for 4 checkers on the left.
Move the checkers so that all the white ones will end on the left, followed by all the black ones. The checkers must be moved in pairs, taking 2 adjacent checkers at a time, without disturbing their order, and sliding them to a vacant place. To solve this problem, only three such moves are necessary.
Start: [ ] [ ] [ ] [ ] [X] [O] [X] [O] [X] [O]
Move 1: [ ] [ ] [O] [X] [X] [ ] [ ] [O] [X] [O]
Move 2: [ ] [ ] [O] [X] [X] [X] [O] [O] [ ] [ ]
Move 3: [O] [O] [O] [X] [X] [X] [ ] [ ] [ ] [ ]
4. Three Moves
Place three piles of matches on a table, one with 11 matches, the second with 7, and the third with 6. You are to move matches so that each pile holds 8 matches. You may add to any pile only as many matches as it already contains, and all the matches must come from one other pile. For example, if a pile holds 6 matches, you may add 6 to it, no more or less. You have three moves.
Start: [11 matches] [7 matches] [6 matches]
Move 1: [4 matches] [14 matches] [6 matches] -> move 7 from the 11 pile
Move 2: [4 matches] [8 matches] [12 matches] -> move 6 from the 14 pile
Move 3: [8 matches] [8 matches] [8 matches] -> move 4 from the 12 pile