Puzzle Sum 4
What two birds do these sums spell?
SOLUTION
LACE – ACE + ARK = LARK
SPEAR – EAR + BARROW – B = SPARROW
Category: Puzzles
Samuel Loyd (1841 – 1911), born in Philadelphia and raised in New York City, was an American chess player, chess composer, puzzle author, and recreational mathematician. As a chess composer, he authored a number of chess problems, often with interesting themes. At his peak, Loyd was one of the best chess players in the US and was ranked 15th in the world, according to chessmetrics.com.
Pirate’s Treasure
Five pirates steal a treasure which contains 100 gold coins. The rules for splitting the treasure among the pirates
- The oldest pirate proposes how to split the money.
- Everybody votes, including the proposer.
- If there are more than 50% negative votes, the proposer gets thrown in the water and the procedure repeats.
Given that the pirates are very smart and bloodthirsty (if they can kill another without losing money, they will do it), how should the oldest pirate suggest to split the money among the five of the in order to maximize his profit?
SOLUTION
Solve the problem backward. Let the pirates be called A, B, C, D, E, where A is older than B, B is older than C, C is older than D and D is older than E.
If there are only two pirates left – D and E, then the D will keep all the treasure for himself.
If there are three pirates left – C, D, and E, C can propose to give just 1 coin to E and keep the rest for himself. Pirate E will agree because otherwise, he will get nothing.
If there are four pirates left – B, C, D, and E, then B can propose to give just 1 coin to D and keep the rest for himself. Pirate D will agree
Now if there are five pirates – A, B, C, D and E, A should give coins to at least two other pirates, because otherwise at least three of them will vote negative. Clearly, B will always vote negative, unless he gets offered 100 coins and D will also vote
Slowest Horse
Two friends made a bet whose horse is slower. After wondering for days what is the fastest and fairest way to figure out who wins the bet, they finally decided to ask a famous wise hermit for help. Upon giving them his advice, the two friends jumped on the horses and started racing back to the city as fast as they could. What did the hermit say?
SOLUTION
He told them to switch their horses and whoever gets to the city first will win the bet.
Sisters and Brothers
In one family there are 6 sisters and each of them has one brother. How many children are there in the family?
SOLUTION
There is just one brother and therefore there are 7 children in the family.
A Maze Puzzle for the Day
Here’s a little maze puzzle I originally built a couple of years ago, that seems apropos to reprise now:
Can you make it from the A in the top left of this grid to the Z in the bottom right, always going either up one letter (for instance, A to B or G to H) or down one letter (for instance, N to M)? The alphabet wraps around, so you can go from Z up to A or A down to Z too. Try as hard as you can (and remember that you can always work backward if you get stuck forwards), and see where you get!
Remark: Solving the maze is not the same thing as solving the puzzle. Read those instructions carefully!
SOLUTION
Notice this puzzle is published on April 1st. Actually, it doesn’t have a standard solution. If you connect every two consecutive letters which appear next to each other in the grid, you will get two disconnected components, one of which contains the START and the other contains the END. The first component has 5 dead-ends – at letters A, P, R, I, L, and the second component has 5 dead-ends – at letters F, O, O, L, S. These two spell out “April Fools”, which is the real solution of the maze.
How Many Letters
How many letters does the correct answer to this puzzle contain?
SOLUTION
Four – the only number which has the same number of letters as the number itself.
Seven Bridges
This is a map of old-time Kongsberg. The green shapes are bridges which connect the different parts of the city. Can you find a path through the city which goes through every bridge exactly once?
SOLUTION
No, you cannot. Notice that, except for the first city and the last city section you finish, the number of bridges used in every other section is even. However, there are three sections with an odd number of bridges, and therefore you cannot use all bridges exactly once.
Illusion Maze
Find a path between the two squares in this Illusion Maze, created by Dave Phillips.
SOLUTION
The solution is shown below.
Funky Mate
Place only 2 rooks and 1 knight on the board, so that the Black player is mated.
SOLUTION
You can place the rooks on c5 and e5, and the knight on f5.
Puzzle Sum 3
What two Italian cities do these sums spell?
SOLUTION
OVEN – O + ICE = VENICE
REEL – EEL + DOME – D = ROME