Puzzle Sum 28
What animals do these sums spell?
SOLUTION
SLOTH + HARROW – ARROW = SLOTH
FERRULE – RULE + VINE + GARRET – VINEGAR = FERRET
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.
1 to 8 on a Cube
Place the numbers from 1 to 8 on the vertices of a cube so that the sum of the four numbers on every face is the same.
SOLUTION
The solution is shown below:
Sequence 1, 3, 7, 12
Which is the next number in the following sequence:
1, 3, 7, 12, 18, 26, 35, 45, 56, ?
SOLUTION
This is the so called Hofstadter Figure-Figure Sequence.
The sequence of the differences between the consecutive numbers in the original sequence is 2, 4, 5, 6, 8, 9, 10, 11… These are exactly the natural numbers missing from the original sequence. Therefore, the next number should be 56 + 13 = 69.
A Cardinal Points
A cardinal points and says, “thorn, shout, seat, and stew.” Can you explain?
SOLUTION
The sentence is a play on words and anagrams. Thorn, shout, seat, and stew are anagrams of the four cardinal directions of the compass: north, south, east, and west.
One Hundred Rooms
There are 100 rooms in a row in a building and inside each room there is a lamp that is turned off. One person enters each room and switches the lamp inside. Then, a second person enters every second room (2, 4, 6, etc.) and switches the lamp inside. A third person switches the lamp in every third room and so on and so far, until person #100 switches the lamp in room 100. How many lamps are turned on at the end?
SOLUTION
We can see that the only switches that have been switched an odd number of times are the ones in rooms with perfect square numbers.
Indeed, if person N has switched the switch in room M, then person M/N has done that as well. Since person N and M/N coincide only when M=N², the claim above follows.
We conclude that the number of lamps that are turned at the end is equal to the number of perfect squares less than or equal to 100; that is exactly 10 rooms.
Conflicting Words
What unique feature do the following words share?
FRIEND, FEAST, THERE, THOROUGH, FLIGHT, WONDERFUL, RESIGN, ENDURING, PEST, COVERT
SOLUTION
Each of these words contains its antonym as a sub-word:
FRIEND – FIEND, FEAST – FAST, THERE – HERE, THOROUGH – ROUGH, FLIGHT – FIGHT, WONDERFUL – WOEFUL, RESIGN – REIGN, ENDURING – ENDING, PEST – PET, COVERT – OVERT
Annihilating Matrix
The numbers 1, 2, … , 100 are arranged in a 10×10 table in increasing order, row by row and column by column, as shown below. The signs of 50 of these numbers are flipped, such that each row and each column have exactly 5 positive and 5 negative numbers. Prove that the sum of all numbers in the resulting table is equal to 0.
SOLUTION
Represent the initial table as the sum of the following two tables:
Since the sum of the numbers in each row of the first table is equal to 0 and the sum of the numbers in each column of the second table is equal to 0, it follows that the sum of all numbers in both tables is equal to 0 as well.
Source:
Quantum Magazine, November-December 1991
Make Me, Save Me, Waste Me, Raise Me
People make me, save me, waste me, raise me. What am I?
SOLUTION
The answer is MONEY.
Movie Conundrums 9
Can you recognize which famous movies are depicted by these images?
SOLUTION
- Snakes on a Plane
- Independence Day
- Mean Girls
- Paths of Glory
- 8 Mile
- The Matrix Revolutions
- Field of Dreams
- Alpha and Omega
- The Thirteenth Floor
- The Sum of All Fears
