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NMSR PUZZLES

 

Send Puzzle Answers To:

WebMaster Dave Thomas, nmsrdaveATswcp.com (Help fight SPAM!  Please replace the AT with an @ )

WHEN ARE PUZZLES UPDATED?

Since they are tied to our hard-copy newsletter and monthly meetings, look for Puzzle Updates, usually on the Friday before the Second Wednesday of each Month!

Next Puzzle Posting:  May 16th (or so), 2008

 

APRIL '08 PUZZLE - "JACKS OF THREE TRADES"

Submitted by Dave Thomas

The MegaGenomics Corporation placed a want ad for a position requiring knowledge of biology, mathematics and computer science. Of the 60 respondents who submitted applications, 46 had training in biology, 40 had training in mathematics, 43 had training in computer science, and 10 had no training in either biology, mathematics or computer science. There are three times as many applicants with mathematics-only backgrounds as with computer-science-only backgrounds; and, there are twice as many applicants with biology-only backgrounds as with computer-science-only backgrounds.

The April Bonus: How many of the applicants had undergone training in all three fields?

Hall of Fame (April Puzzle Solvers):
Steve's Brother in Law (CA)
K Sengupta (Calcutta,INDIA)
Keith Gilbert (NM)
Eric Hanczyc (WA)
Eugene Aronson (NM)
Ross Goeres (NM)

 

MARCH '08 PUZZLE - "CORDIALITY BEFORE CORDIALS"

Submitted by Ken Lynch

A party of three couples (Ben and Alice being one couple) enters a room and shakes hands based on these conditions: a) Once you shake a person's hand, you do not shake with that person again. b) Couples do not shake hands with each other. Alice asked each person how many hands he/she shook, and everyone gave her a different answer.

The March Bonus: How many hands did Ben shake?

Hall of Fame (March Puzzle Solvers):
Steve's Brother in Law (CA)
K Sengupta (Calcutta,INDIA)
Eugene Aronson (NM)
Ross Goeres (NM)
Eric Hanczyc (WA)

 

FEBRUARY '08 PUZZLE - "Playing with Fire"

Submitted by Paul Braterman

Can you arrange five matches so that each of them touches three and only three others? The matches may touch at any point, but you are not allowed to bend or break them.

Hall of Fame (February Puzzle Solvers):
Steve's Brother in Law (CA)
K Sengupta (Calcutta,INDIA)
Eugene Aronson (NM)
Eric Hanczyc (WA)
Ross Goeres (NM)
Bob Schmidt (NM)

 

JANUARY '08 PUZZLE - "The Flower and the Lake"

Submitted by Dave Thomas, after Longfellow

A long-stemmed flower extends straight up from the bottom of a lake, extending 8 inches above the lake’s surface. A man in a rowboat observes that, when he pulls on the flower, it touches the lake’s surface at a distance of 20 inches from the stem’s original position.

The January Bonus: how deep is the lake?

Hall of Fame (January Puzzle Solvers):
Rocky S. Stone (Tijeras, NM)
Steve's Brother in Law (CA)
K Sengupta (Calcutta,INDIA)
Keith Gilbert (NM)
Ross Goeres (NM)
John Lopez (NM)
Paul Braterman (NM)
TSgt Michael K Stage(NM)

 

DECEMBER '07 PUZZLE - "The Crazy Clocks"

Submitted by Dave Thomas

Based on a True Story!

On the long drive home from a field trip to fabled Shark Tooth Ridge, a paleontologist passenger observes a discrepancy between the car’s digital clock and his cell phone’s digital clock. Both clocks show hours and minutes only. Sometimes the cell phone reads two minutes ahead of the car’s clock, and sometimes it reads just one minute ahead.

The December Bonus:If the clocks appear to be two minutes apart for twice as long as they appear to be one minute apart, and assuming both clocks can keep perfect time, what is the actual time difference (in seconds) between the clocks?

Hall of Fame (December Puzzle Solvers):
K Sengupta (Calcutta,INDIA)
Steve's Brother in Law(CA)
Eugene Aronson (NM)
Ross Goeres (NM)
Nick Seigal (Eugene OR)

 

NOVEMBER '07 PUZZLE - "By The Numbers"

Submitted by Ken Lynch (from Douglas Hofstadter’s Metamagical Themas)

Complete the following sentence: In this sentence, the number of occurrences of 0 is _, of 1 is _, of 2 is _, of 3 is _, of 4 is _, of 5 is _, of 6 is _, of 7 is _, of 8 is _, and of 9 is _. Each blank is to be filled with a numeral of one or more digits, written in decimal notation.

The November Bonus: Find two solutions.

Hall of Fame (November Puzzle Solvers):
K Sengupta (Calcutta,INDIA)
Steve's Brother in Law(CA)
Eugene Aronson (NM)
Ross Goeres (NM)
Charles Vaughn (Rotterdam, NL)

 

OCTOBER '07 PUZZLE - “Super Bounce”

Submitted by Dave Thomas

A large ball and a very small ball are dropped from a height of five feet, as shown. Both balls are perfectly elastic ("bouncy"). When the large ball bounces, it then impacts the small ball, bouncing it upward as shown.

The October Bonus: What is the highest that the small ball can bounce?

(A) 5 feet
(B) 10 feet,
(C) 15 feet,
(D) 20 feet,
(E) 45 feet.

Hall of Fame (October Puzzle Solvers):
K Sengupta (Calcutta, INDIA)
Keith Gilbert (NM)
Eugene Aronson (NM)

 

SEPTEMBER '07 PUZZLE - “Trisecting a Clock Face”

Submitted by Gene Aronson

At what time(s) do the hour, minute, and second hands of a 12-hour clock divide the face into three equal segments, either precisely or as close as possible? Assume a perfectly smooth motion, and answer to within one second.

Hall of Fame (September Puzzle Solvers):
K Sengupta (Calcutta, INDIA)
Ross Goeres (NM)
John Lopez (NM)

 

AUGUST '07 PUZZLE - “Gearing Up for a Mystery!”

Submitted by John Geohegan

Here's a puzzle from chapter 9, "Patterns and Primes", of Martin Gardner's Sixth Book of Mathematical Games from Scientific American:

Shown below are two meshing gears marked with arrows pointing toward each other. The larger gear has 181 teeth.

The August Bonus:

How many turns must the smaller gear make before the arrows again point to each other?

Hall of Fame (August Puzzle Solvers):
Steve's brother-in-law (CA)
K Sengupta (Calcutta, INDIA)
Ross Goeres (NM)
Eugene Aronson (NM)

 

JULY '07 PUZZLE - “The Poorly-Planned Polygraph”

Submitted by Dave Thomas

Paranormal investigator George Bradford had worked for months setting up an elaborate blind test of polygraphs. And here he was at last, taking data from four individuals who had all promised to abide by the strict experimental protocols. The first part of the experiment had all four subjects meet in private, where they witnessed one of their number hide a toy bunny. Then, each subject was told to make two statements to polygraph testers (and other observers) about the "incident": one true, and one false. Only later, as the correct answers were revealed, could the researchers see if the polygraph machines used alongside were giving correct answers or not.

As the four subjects gave their two statements each, George turned white, as he realized that simple logic would allow the polygraph examiners to decide which statements were True or False, making it very easy for them to cheat.

Here are the four pairs of statements:

Arnie said: It wasn't me. It was Carl.

Betty said: It was Arnie. It wasn't Carl.

Carl said: It wasn't Betty. It wasn't Debbie.

Debbie said: It wasn't Carl. It was me!

The July Bonus:

(A) Which are lies, and which are true?

(B) Who hid the bunny?

Hall of Fame (July Puzzle Solvers):
K Sengupta (Calcutta, INDIA)
Steve's brother-in-law (CA)
Ross Goeres (NM)
Roy Thearle (UK)
Eric Hanczyc (WA)
Eugene Aronson (NM)

 

JUNE '07 PUZZLE - “Number Cipher!”

Submitted by Ken Lynch

Consider the following sum:

2831
+ 101461
+ 513122
= 617414

The June Bonus:

(A) Replace each digit with a different digit to make another correct addition problem; no digit may replace itself. It’s a Numerical Cipher!

(B) Can you replace each digit with a letter to spell the names of four of the United States?

Hall of Fame (June Puzzle Solvers):
K Sengupta (Calcutta, INDIA)
Ray Comas (OH)
Ross Goeres (NM)
Eugene Aronson (NM)
Eric Hanczyc (WA)

 

May '07 PUZZLE - “What is the Product?”

Submitted by John Geohegan

The following puzzle is from "The Surprise Attack in Mathematical Problems", by L.A.Graham. Only the words have been changed.

Three digits, a,b,and c have been used to form the three digit numbers abc, bca, and cab, which have then been multiplied to make a 9-digit product. The number 234,235,286 is not the product, but 6 is in the proper place and the other digits are disordered.

The May Bonus: What is the Product?

Hall of Fame (May Puzzle Solvers):
K Sengupta (Calcutta, INDIA)
Ray Comas (OH)
Ross Goeres (NM)
Eugene Aronson (NM)
Eric Hanczyc (WA)
Paul Flocken (NC)

 

April '07 PUZZLE - “Derek's Appointment”

Derek bicycles from Abercrombie to Fitch for a one o'clock appointment. After pedalling at a steady rate for 42 kilometers, he increases his speed by 3 km/hr and arrives at precisely 1:00. If he hadn't increased his speed he would have been 18 minutes late, and if he had made the whole trip at the greater speed he would have arrived, exhausted, 42 minutes early.

The April Bonus: What time did Derek leave Abercrombie?

Hall of Fame (April Puzzle Solvers):
Dave Thomas (NM)
Keith Gilbert (NM)
Ray Comas (OH)
Bob Schmidt (NM)
Ross Goeres (NM)
Eugene Aronson (NM)

 

March '07 PUZZLE - “Alice and Bob and the Tossed Coins”

submitted by Ray Comas (Ohio)

Alice and Bob each have a collection of coins. Alice has one more coin than Bob. Alice tosses all of her coins in the air, and counts how many come up heads. Then Bob does the same with his coins.

The March Bonus: Assuming all coins are fair coins, what is the probability that Alice will produce more heads with her coin toss than Bob does with his coin toss?

Hall of Fame (March Puzzle Solvers):
K Sengupta (Calcutta, INDIA)
Roy Thearle (UK)
Bob Carroll (NY)
Eric Hanczyc (WA)
Paul Braterman (NM)
Keith Gilbert (NM)
Eugene Aronson (NM)
Ross Goeres (NM)

 

February '07 PUZZLE - “SORTING SUNDRY SIBLINGS”

submitted by Dave Thomas

In the family of Steve and Sally Starling, each boy has twice as many brothers as sisters, while each girl has three times as many brothers as sisters.

The February Bonus: How many Starling Siblings are there?.

Hall of Fame (February Puzzle Solvers):
K Sengupta (Calcutta, INDIA)
Ray Comas (OH)
Harry Murphy (NM)
Harold Gaines (KS)
Roy Thearle (UK)
John Geohegan (NM)
Christian Winteler, (Switzerland)
Eric Hanczyc (WA)
Bob Carroll (NY)
Eugene Aronson (NM)
Ross Goeres (NM)
Bob Schmidt (NM)

 

January '07 PUZZLE - “BETTING ON CHUCK-A-LUCK”

submitted by John Geohegan

In the carnival game called Chuck-a-Luck, the player bets on a number, one through six. Three dice are then rolled and if the player's number comes up once, he receives his original bet, for instance a dollar, plus another dollar. If his number comes up two or three times, he receives his original bet plus another two or three dollars. The smooth-talking game operator suggests that since the chance of the chosen number showing up on any die is one out of six, the player has a fifty-fifty chance of getting his number at least once on the three dice, and the payoffs of two or three dollars make the odds to the player's advantage.

But really, how much does the player stand to win or lose on an average bet of one dollar?

Hall of Fame (January Puzzle Solvers):
K Sengupta (Calcutta, INDIA)
Dave Thomas (NM)
Keith Gilbert (NM)
Ray Comas (OH)
Eugene Aronson (NM)
Grey Wolf (anonymous lurker on the Internet)
W. Kevin Vicklund (MI)

 

DECEMBER '06 PUZZLE - "Grazing Grass by the Numbers!"

submitted by K Sengupta (Calcutta, INDIA)

A grassland can support 63 sheep for 5 days; or, 22 cows for 9 days; or, 16 cows and 5 sheep indefinitely. The grass grows at a constant rate per unit time in the grassland.

Three friends Pedro, Quentin and Rhett jointly hire the grassland for $6930. They agree that the share of rent paid by any given friend would be determined in accordance with the total amount of grass consumed by his pets.

Pedro grazes 9 cows and 16 sheep for a period of 20 days; Quentin grazes 10 cows and 3 sheep for 28 days and, Rhett grazes 6 cows and 13 sheep for 27 days.

The December Bonus: Determine the respective share of rent payable by Pedro, Quentin and Rhett on the grassland from the information inclusive of the foregoing statements.

Hall of Fame (December Puzzle Solvers):
John Geohegan (NM)
Ray Comas (OH)
Eugene Aronson (NM)

 

NOVEMBER '06 PUZZLE - "Squaring,Cubing,Ten Digits -Oh My!"

submitted by John Geohegan

The square and the cube of a certain whole number can be written using each of the ten digits, 0 through 9, exactly once.

The November Bonus: What is that certain number?

Hall of Fame (November Puzzle Solvers):
K Sengupta (Calcutta, INDIA)
Harold Gaines (KS)
Ray Comas (OH)
Eric Hanczyc (WA)
Eugene Aronson (NM)
Bob Schmidt (NM)

 

OCTOBER '06 PUZZLE - "Starting the Election Party"

submitted by Dave Thomas

It is Election Night, and candidate Bill E. Bob is pacing around election headquarters. With 60% of precincts reporting, Bob is leading with 60% of the vote.

The October Bonus:

(a) If only half of the remaining voters (40% of precincts) vote for Bob, will he win?

(b) At what percentage of precincts reporting will Bill E. Bob be justified in popping the cork off of a champagne bottle?

Hall of Fame (October Puzzle Solvers):
W. Kevin Vicklund (MI)
Grey Wolf (anonymous lurker on the Internet)
K Sengupta (Calcutta, INDIA)
Eric Hanczyc (WA)

 

SEPTEMBER '06 PUZZLE - "FAIR TOSSES"

submitted by Ken Lynch

Alice and Bob toss a fair coin alternately to play a game where the first to toss "heads" immediately after the other tosses a "tail" wins. Alice tosses first.

The September Bonus: What is the probability that:

a) Alice wins on her 1st toss

b) Bob wins on his 1st toss

c) Alice wins on her 3rd toss

d) Bob wins on his 5th toss

e) Alice wins.

Hall of Fame (September Puzzle Solvers):
K Sengupta (Calcutta, INDIA)
Eric Hanczyc (WA)
W. Kevin Vicklund (MI)
Harold Gaines (KS)
Eugene Aronson (NM)

 

AUGUST '06 PUZZLE - "THE PIRATE CHEST"

submitted by Dave Thomas

You have been captured by Pirates while sailing the Carribean, and have been brought before their gruff Captain. With a sinister snarl, he barks "I've a chest here that holds 120 pounds of pure gold coins. Some of these coins be decloons [10 ounces each], and the rest be triploons [three ounces each]. Now, mate, if ye can tell me exactly how many decloons and triploons are in my chest, ye walks away a free man. Get it wrong, and ye'll be walkin' the Plank!" After another pirate suggested that the riddle was perhaps overly challenging, the Captain snorted, and then offered a hint: "Awright, matey - the number of decloons times the number of triploons couldn't be larger!"

The August Bonus: For your life - how many decloons and how many triploons are in the chest?

Hall of Fame (August Puzzle Solvers/HONORARY PIRATES):
Jesse Johnson (NM)
K Sengupta (Calcutta, INDIA)
Bob Carroll (NY)
Harold Gaines (KS)
Jim Mitchell (NM)
Eric Hanczyc (WA)
Ross Goeres (NM)
Ken Lynch (TX)
Ray Comas (OH)
Eugene Aronson (NM)
Grey Wolf (anonymous lurker on the Internet)
Marek Ctrnact (Czech Republic)
Jeff Elliott (Spanish colony of California)
Christian Winteler (Switzerland)
John M. Sovitsky (VA)
Roy Thearle (UK)
W. Kevin Vicklund (MI)
Calum mac Leoid (Pentamere)

 

JULY '06 PUZZLE - "THE LAW OF AVERAGES "

submitted by Dave Thomas & Ross Goeres

In a race along a two-kilometer-long track, you are required to travel the first kilometer at an average speed of 20 km/hour.

The July Bonus: (A) How fast must you travel on the second kilometer of track to achieve an overall average speed of 30 km/hour? (What's your off-the-hip estimate? And your Final Answer?) (B) How fast must you travel on the second kilometer of track to achieve an overall average speed of 40 km/hour? (C) What have you learned, Grasshopper, about trying to average ratios?

Hall of Fame (July Puzzle Solvers):
Bob Carroll (NY)
Jen Niver (NM)
Eric Hanczyc (WA)
Eugene Aronson (NM)
Harold Gaines (KS)
Keith Gilbert (NM)
K Sengupta (Calcutta, INDIA)

 

JUNE '06 PUZZLE - "TOUCHED BY A TEN-FOOT POLE "

submitted by Gene Aronson

(Gene Aronson has submitted the following problem in slightly different form )

Mathematicians have shown that the following problem is workable, even though it looks like more information might be necessary. Knowing that it's workable makes it much easier to find the numerical answer.

A ten-foot pole floats in a large swimming pool shaped approximately as shown in the sketch below. As the pole makes one circuit around the pool (BLACK boundary), both ends of the pole bump continuously against the wall. During this circuit, point P on the pole, six feet from one end, traces out the smaller area labelled A (RED boundary).

.

HOW MUCH SMALLER than the pool, in square feet, is area A?

Hall of Fame (June Puzzle Solvers):
Harold Gaines (KS)
K Sengupta (Calcutta, INDIA)
Gene Delloro (Toronto, ON)
Eric Hanczyc (WA)
Bob Carroll (NY)

 

MAY '06 PUZZLE - "Mr. Auber and Mr. Benatar "

submitted by K Sengupta of Calcutta, INDIA

The Identification (ID) Numbers allotted to Mr. Auber and Mr. Benatar are such that the numerical magnitude of the ID number allotted to Mr. Benatar is greater by 10 than the numerical magnitude of the ID number allotted to Mr. Auber. None of the two ID numbers contained any leading zeroes.

A mutual acquaintance, Mr. Cavalli , who is aware of the above facts ( but doesn't know the actual ID numbers of the two gentlemen), queried Mr. Auber and Mr. Benatar in turn about the sum of the digits in their ID Numbers. The responses elicited by him were respectively 44 and 27.

At this point, Mr. Cavalli requested Mr. Auber and Mr. Benatar give some additional information. Both gentlemen answered with a new question: "What are the smallest possible values for the two ID numbers?"

Thereafter, Mr. Cavalli was able to ascertain precisely the ID numbers of Mr. Auber and Mr. Benatar.

Then, The ID # of Mr. Auber = ? and, The ID # of Mr.Benatar = ?

Hall of Fame (May Puzzle Solvers):
Aaron Sullivan (AZ)
Harold Gaines (KS)
Eric Hanczyc (WA)
Bob Schmidt (NM)

 

APRIL '06 PUZZLE - "CIPHER ADDITION..."

submitted by John Geohegan

Here's an addition cryptarithm sent in by Ken Lynch. Difficult as it is to solve, composing it seems close to a miracle.

A P P R E C I A T I V E

+ I N C A P A C I T A T E

+ I N D E P E N D E N C E

= P A R T I C I P A T E D

Hall of Fame (April Puzzle Solvers):
Ross Goeres (NM)
Harold Gaines (KS)
Eric Hanczyc (WA)
Eugene Aronson (NM)
Mike Denny (AZ)
Bob Schmidt (NM)

 

MARCH '06 PUZZLE - "The Race of the Weights..."

submitted by John Geohegan

Weight-driven grandfather clocks use two weights. One drives the pendulum and causes the hands to turn, the other supplies power when the clock strikes either the hour or the half-hour. Problem #20 in L. A. Graham's "Ingenious Mathematical Problems and Methods" reads, "A weight-driven clock, striking the hour, and a single stroke for the half hour, is wound at 10:15 P.M. by pulling up both weights until they are exactly even at the top. Twelve hours later, the weights are again exactly even, but lowered 720 mm. What is the greatest distance they separated during the interval?"

Hall of Fame (March Puzzle Solvers):
Dave Thomas (NM)
Ross Goeres (NM)
Harold Gaines (KS)
Eugene Aronson (NM)
Eric Hanczyc (WA)
Mike Denny (AZ)

 

FEBRUARY '06 PUZZLE - "My Candle Burns at One End..."

submitted by John Geohegan

Two “identical” candles are lighted at the same time. One will burn out in five hours, the other in eight hours. How long will it be before one is 2.2 times the length of the other, if (a) “identical” means the candles burn at the same rate, and start out having different lengths, AND (b) “identical” means the candles start out having the same lengths, and burn at different rates?

Hall of Fame (February Puzzle Solvers):
William Decorie (IL) (b)
Ross Goeres (NM) (a,b)
Keith Gilbert (NM) (a,b)
Harold Gaines (KS) (a,b)

 

JANUARY '06 PUZZLE - "SCALING UP"

submitted by Dave Thomas

A brilliant but warped scientist is persuaded to help a Hollywood mogul make a "King Kong" sequel, not by creating a giant ape, but by developing miniature humans, just one-hundredth their normal height. Designers have crafted a one-hundredth-scale set for the tiny humans to interact with a normal, life-sized gorilla.

The January Bonus (Warning - SPOILER!!) In Kong's fall from the scaled-down Empire State building, how many times faster than normal should the film be shot to give Kong a proper-looking plummeting rate?

Hall of Fame (January Puzzle Solvers):
William Decorie (IL)
John Geohegan (NM)
Harold Gaines (KS)

 

DECEMBER '05 PUZZLE - "CAPACITY"

submitted by Dave Thomas

Paul lives in Española, where the price of gasoline is $2.50 per gallon. There is a gas station near Albuquerque, 75 miles from Paul's house, which sells gas at $2.00 per gallon; his truck gets 30 miles per gallon. Paul schemes to save money by buying gas at the cheaper station in Albuquerque, and then cruising around his Española home.

The December Bonus: What is the minimum number of gallons that Paul's gas tank(s) would have to hold in order for his scheme to be feasible?

Hall of Fame (December Puzzle Solvers):
William Decorie (IL)
Bob Schmidt (NM)
John Geohegan (NM)
Ken Lynch (TX)

 

NOVEMBER '05 PUZZLE - What's Left Behind?

submitted by John Geohegan

A hole six inches long is drilled straight through the center of a solid sphere.

The November Bonus: What is the volume of the remaining material?

Hall of Fame (November Puzzle Solvers):

William Decorie (IL)
Bob Schmidt (NM)
Keith Gilbert (NM)
Click HERE for the Answer

 

OCTOBER '05 PUZZLE - Double Sixes

submitted by John Geohegan

In 1654, Chevalier de Méré approached Blaise Pascal with a question about a gambling game that had been played for hundreds of years. The house would bet even money that a player would roll at least one double-six in 24 rolls of a pair of dice.

The October Bonus: Did the house stand to make money on this bet?

Hall of Fame (October Puzzle Solvers):
William Decorie (IL)
Bob Schmidt (NM)
Ross Goeres (NM)
Ken Lynch (TX)

 

SEPTEMBER '05 PUZZLE - The Mirror of Time

submitted by John Geohegan

Mike's age is multiplied by seven if its digits are reversed, and one more digit is inserted. How old is Mike?

The September Bonus: How old is Mike?

Hall of Fame (September Puzzle Solvers):
William Decorie (IL)
Barry Spletzer (NM)
TexasSkeptic  (TX)
Bob Schmidt (NM)
Charles E. Oelsner (NM)
Kevin Webster (NM Lobo in WA)
Ken Lynch (TX)

 

AUGUST '05 PUZZLE - The Bargain Sale

Courtesy Sam Loyd

In describing his experiences at a bargain sale, Smith says that half his money was gone in just thirty minutes, so that he was left with as many pennies as he had dollars before, and but half as many dollars as before he had pennies.

The August Bonus: Now, how much did Smith spend?

Hall of Fame (August Puzzle Solvers):
John Geohegan (NM)
William Decorie (IL)
Eric Hanczyc (WA)
Charles E. Oelsner (NM)
Keith Gilbert (NM)
Bob Schmidt (NM)
TexasSkeptic  (TX)

 

JULY '05 PUZZLE - SELF-DIVISIBLE NUMBERS

Submitted by John Geohegan

New Scientist magazine publishes a new Enigma(math puzzle) each week. In the June 4 issue, the puzzle is to find the largest integer whose digits are all different (and do not include 0) that is divisible by each of its individual digits. Thus the number 248 is divisible by 2, 4, and 8 but so is 824 which is larger. The largest such integer is MUCH less than 987,654,321. Next month the solution will show how to cut this problem down to a reasonable size.

The July Bonus: What is the largest such integer?

Hall of Fame (July Puzzle Solvers):
William Decorie (IL)
TexasSkeptic  (TX)
Charles E. Oelsner (NM)
Ken Lynch (TX)

 

JUNE '05 PUZZLE - THE NO-COMMISSION BROKER

Submitted by Dave Thomas

There was once a broker of Yeti fur, highly prized for its luxuriant texture. This broker boasted that he took no commissions when either buying or selling the fur. The townsfolk wondered how he could possibly stay in business, but he was apparently quite prosperous. After years had passed, they finally found out the broker's secret -- he was caught using a biased scale. The rigged scale was arranged to be an ounce per pound short when buying, and an ounce per pound heavy when selling. The broker's final transaction involved an amount of Yeti fur that would have given him $30.00 of illicit profit.

The June Bonus: How much did the broker spend when buying the fur for his last transaction?

Hall of Fame (June Puzzle Solvers):
M. K. Johnson (NM)
John Geohegan (NM)
Harold Gaines (KS)
TexasSkeptic  (TX)
Pierre Scalise (AL)
Keith Gilbert (NM)
Ken Lynch (TX)

 

MAY '05 PUZZLE - THE MICRO-BREWMASTER

Submitted by TexasSkeptic

The Brownbagg Brewery's signature beer, Bob Brownbagg Barleywine, uses three strains of hops (Bitterbit, Flowergirl and Aromaroma) and three types of barley malt (Pale, Toasted and Burnt). The hops contribute Bitter, Aromatic, and Floral flavor fractions to the "wort" (unfermented beer syrup); the grains contribute color, complex carbohydrates ("unfermentable sugars") and glucose/maltose ("fermentable sugars"). Fermentation converts all the glucose/maltose into alcohol, one kg producing 500 ml of alcohol. The other components are not affected.

Grain yields

One kilogram of this grain
Pale Barley
Toasted Barley
Burnt Barley
produces this much fermentable sugar (g)
600
100
0
this much complex carbohydrate (g)
100
500
0
and this many units of color
0
100
600

Hops yields

One gram of this strain
Bitterbit
Flowergirl
Aromaroma
produces this much Bitter fraction (mg)
50
10
20
this much Aromatic fraction (mg)
20
30
60
and this much Floral fraction (mg)
30
70
30

The final product contains (per liter):

103.7 ml alcohol
51 g complex carbos
18.4 units color
72 milligrams Bitter fraction
86 mg Aromatic fraction
96 mg Floral fraction
And the Balance, water

The May Bonus: How much of each grain type and hop strain must the brewmaster purchase for one 6500 liter batch of Bob Brownbagg Barleywine?

Hall of Fame (May Puzzle Solvers):
Dave Thomas (NM)
Ken Lynch (TX)
Ross Goeres (NM)
John Geohegan (NM)
William J.Keith (PA)

 

APRIL '05 PUZZLE - JUGS

Submitted by Dave Thomas

World-renowned chemist Dr. Dweeb owned a 12-gallon jug full of sulfuric acid, and another smaller jug. He liked to make up his favorite 25% strength solution (with a quarter of the solution being H2SO4, and the rest good old H2O) with a curious procedure: first, he poured acid from the 12-gallon jug to fill the smaller jug, and then he topped off the big jug with water. After the acid and water had been thoroughly mixed in the big jug, he drew off another small jugful, and again topped off the large jug with more water, arriving at his 25% solution.

The April Bonus: What's the capacity of the smaller jug?

Hall of Fame (April Puzzle Solvers):
Keith Gilbert (NM)
John Geohegan  (NM)
Bob Wood  (NM)
TexasSkeptic  (TX)
Harold Gaines (KS)
Ken Lynch (TX)

 

MARCH '05 PUZZLE - RACE AGAINST TIME

Submitted by Dave Thomas

This month's puzzle might just be harder than it may at first appear! It seems that two brothers from the famous puzzle-solving Answer family, Bobby and Al Answer, were trying out some new hot rod cars on the family's private race-track. Once both racers were up to their respective speeds (Bobby's car was going 120 miles per hour, and Al's was going 95 mph), they crossed the starting mark of the two-mile track just as the gun went off, and then maintained their respective speeds for 24 laps each.

The March Bonus: How much time passes until Bobby first catches up to Al?

At what position on the two-mile track (relative to the starting mark) does this occur?

Hall of Fame (March Puzzle Solvers):
Jesse Johnson (NM)
TexasSkeptic (TX)
Keith Gilbert (NM)
Ken Lynch (TX)
John Fleck (NM)

 

FEBRUARY '05 PUZZLE - THE BIG BEER BASH

Submitted by Dave Thomas

This month's puzzle is for today's mathematically-minded college frat rats and party-goers. The Kappa Kuppa K'rona fraternity was planning for the Big Bash. Usually, 10 cases of Spud Beer, which is 6 and 1/4 % alcohol by volume, are required for the Bash. (There are four 6-packs per case, and 12 ounces per beer, of course!). This year, however, crafty funds manager George Waldo Busch calculated that they wouldn't need to buy as many cases if they got "Beastie Beer" instead, since that brand has a mind-numbing 15 and 5/8% alcohol by volume.

The February Puzzle: How many cases of "Beastie Beer" should Busch Buy for the Big Bash?

Hall of Fame (February Puzzle Solvers):
John Geohegan (NM)
Marilyn Goodrich (NM)
TexasSkeptic (TX)
Harold H. Gaines (KS)
Mike Arms (NM)
Ken Lynch (TX)

 

JANUARY '05 PUZZLE - SOLVE FOR X

Submitted by John Geohegan

Fill in the x's with digits.

Hall of Fame (January Puzzle Solvers):
Marilyn Goodrich (NM)
Rod Earwood (NM)
Mark Maravetz (NM)
Ken Lynch (TX)

 

 

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