CHAPTER 1 Flashcards
RUFUS T. FLYPAPER THE DRIVER
Rufus T. Flypaper drives two miles to work every morning. Very precise, he knows he must average 30 mph to arrive on time. One morning a woman driver impedes him for the first mile, cutting his average to only 15 mph. He quickly calculated his proper speed for the rest of his trip to arrive on time. Assume that his car could do 120 mph. Could he arrive on time?
- Could he arrive on time?
- used minutes? and for how many miles?
- No
- he has already used 4 minutes (time that he has to go the whole 2 miles.)
A HUNTER WITH ONE-PIECE RIFLE
A hunter wished to take his one-piece rifle on a train but the conductor refused to permit it in the coach and the baggage man could not take any article whose greatest dimension exceeded 1 yard. The length of the rifle was 1.7 yards. What could the hunter do?
* What could the hunter do?
* length on a side?
- He could put his gun diagonally in a cubical box,
- 1 yard on a side
SOUTH AMERICAN BOTFLY
Stations A and B are 120 miles apart on a single-track railroad. At the same time that a train leaves A for B at 25 mph, a train leaves B for A at 15 mph. Just as the first train leaves A, a South American botfly flies from the front of the engine straight toward the other train at 100 mph. On meeting the second train it immediately turns back and flies straight for the first train. It continues to fly back and forth with undiminished speed until it is crushed in the eventual collision. How far had the fly flown?
- How far had the fly flown?
- 300 miles
A MAN WALKS SOUTH, WEST, NORTH
A man walks one mile south, one mile west, then one mile north, ending where he began. From how many points on the surface of the eartn can such a journey be made?
- how many points on the surface of the eartn can such a journey be made?
- infinity of points
STOGEY GAME
In the game of “Stogey” two players alternately place cigars on a rectangular table with the restriction that each new cigar must not touch any of the previously placed cigars. Can the 1st player assure himself of victory if we define the loser as the first player who finds himself without sufficient room to place a cigar?
- Can the 1st player assure himself of victory?
- Placement of cigar?
- Counter?
- Yes
- place cigar vertically on its flat end at the center of the table
- counter each opponent’s moves by reflecting them through the center of the table
BRICKLAYER, FIND HEAVIEST BRICK
A bricklayer has 8 bricks. Seven of the bricks weight the same amount and 1 is a little heavier than the others. if the man has a balance scale how can he find the heaviest brick in only 2 weighing?
- 3 groups of bricks (3,3,2)
-
Weighs 2 sets of 3 bricks
if balance - heaviest brick is in the group containing 2 brick.
if not balance - weighs 2 bricks from the heavier group. if balance, heaviest brick is set aside. if not, the scale will tell the heaviest brick.
MAYNARD’S GRANDFATHER CLOCK
Maynard’s Grandfather Clock is driven by two weights, one for the striking mechanism which strikes the hours only, the other for the time mechanism. When he hears the clock strike his bedtime, he immediately winds the clock and retires. After winding, the weights are exactly opposite each other. The weights are again opposite every six hours thereafter. What is Maynard’s bedtime?
Maynard must retire (go to bed) at 9 p.m. or 3 a.m.
REVERSE TIC-TAC-TOE
The game of reverse tic-tac-toe (known to some as toe-tac-tic) has the same rules as the standard game with one exception. The first player with three markers in a row loses. Can the player with the first move avoid being beaten?
- Can the player with the first move avoid being beaten?
- first mark placement?
- counter?
- Yes
- take center square
- counter opponent’s moves by taking diametrically opposite square
IS IT POSSIBLE TO MOVE THE KNIGHT TO ALL SQUARES?
Using graph paper to simulate a board of 64 squares and starting anywhere, is it possible to move a Knight to all squares without touching the same square twice? Move can be made from A to either B.
- Is it possible to move a Knight to all squares without touching the same square twice?
- Solution?
- Yes
- Many Solution
DR. FURBISHER IS BUYING SOMETHING…
Dr. Furbisher LaRouche, the noted mathematician, was shopping at a hardware store and asked the price of certain articles. The salesman replied, “One would cost 10 cents eight would cost 10 cents, seventeen would cost 20 cents, one hundred and four would cost 30 cents, seven hundred and fifty six would also cost 30 cents, and one thousand and seventy two would cost 40 cents. What was Dr. LaRouche buying?
- What was Dr. LaRouche buying?
- Price per item?
- Dr. LaRouche was buying numbers (for doors, gates, etc.)
- 10 cents per digit.
NONPRIME NUMBERS
Find 1000 consecutive nonprime numbers.
- general equation?
- 3 conditions?
- 1 example?
Example: 1001! + 2; 1001! + 3,… , 1001! + 1001.
General: n! + A
* this is shall be divisible by A
* A > 1
* A < (n + 1)
2 OPPOSITE SQUARE REMOVED FROM CHECKERBOARD
Two squares are removed from opposite corners of a checkerboard leaving 62 squares. Can the checkerboard be filled with 31 dominoes, each domino covering two adjacent squares?
- Can the checkerboard be filled with 31 dominoes?
- how many squares for each color?
- condition of domino covering square?
- NO
- 32 squares of one color and 30 squares of another color.
- each domino only covers one square of each color.
SUN RISES
Assuming the sun rises at 6:00 a.m., sets at 6:00p.m., and moves at a uniform rate. how can a lost boy scout determine south by means of a watch on a cloudless day?
- how can a lost boy scout determine south by means of a watch on a cloudless day?
- where is south
- Align the hour hand with the sun’s azimuth
- South will be between the hour hand and 12.
OTTFFSSE
What letter follows OTTFFSSE?
- N
- first letter of numbers
THREE GROUPS OF NUMBER
The numbers are divided into three groups as follows: 0,3,6,8,9,… in the first group, 1,4,7,11,14,… in the second group and 2,5,10,12,13,… in the third. In which groups would 15,16 and 17 be placed?
- 15 and 16 - 3rd group
- 17 - 2nd group
1st group - numbers with curve lines only
2nd group - numbers with straight lines only
3rd group - numbers with both straight and curve lines
PITCHES MADE BY HI N. OUTSIDE
In a fast Major League baseball game, pitcher Hi N. Outside managed to get by with the minimum number of pitches possible. He played the entire game, which was not called prior to completion. How many pitches did he make?
- How many pitches did he make?
- 4 conditions
- 25
conditions:
* he must be in the losing side
* allowed atleast 1 home run
* required atleast 1 pitch
* 24 more pitches for 24 outs
12, 1, 1, 1
Determine the next three terms of the sequence 12, 1, 1, 1, ….
- next three terms?
- pattern?
- 2, 1, and 3
- sequence represents the number of chimes of a wall clock which strikes once on the half hour.
23-LINK CHAIN
What is the least number of links that must be disengaged from a 23-link chain so that any number of links from 1 to 23 can be obtained by taking one or more of the piece.
- how many links?
- link’s placement?
- 2 links
- 4th and 11th
SET A AND B OF INTEGERS
The set A contains the integers 0,4,5,9,11,12,13,14,19,… The set B contains 1,2,3,6,7,8,10,15,16,17,18,… Place 20 and
21 in their proper sets.
- 20 - set A
- 21 - set B
Set A - contains numbers with even quantity of letters in their name. (e.g. Zero - 4 letters)
Set B - contains numbers with odd quantity of letters in their name (e.g. One - 3 letters)
STATE UNIVERISITY QUARTER SCORES
State University won their first football game of the season 17 to 0. Though they scored no safeties, they managed to score more points each quarter than they had scored in the previous quarter. What were State’s quarter scores?
- 0, 3, 6, 8
(every quarter in order, without safeties)
3rd quarter - points either from 1 touchdown or 2 field goals
4th quarter - points from 1 touchdown + 2 point conversion.
CHEMIST WITH 54 cc. ELIXER
A chemist has three large test tubes and a beaker with 54 c.c. of elixir. Using the test tubes and ingenuity only, how can he retain
50 c.c. in the beaker?
- 54 divide to 2 tubes (27 | 27 | 0), return 27 to beaker (sum: 27)
- 27 divide to 3 tubes (9 | 9 | 9), return 18 to beaker (sum: 45)
- 9 divide to 3 tubes (3 | 3 | 3), return 6 to beaker (sum: 51)
- 3 divide to 3 tubes (1 | 1 | 1), return 1 to beaker (sum: 52)
- Spill 2 from 52, gives you 50
=6.3l
=6.3l
Using only the above symbols three valid equations are possible.
- 6=3!
- ω^6 = 1.
- ω^9 = 1.
ω is a notation for one of the complex cube roots of 1
