Saturday, 4 June 2016

DAY 447

THREE COINS

Credit: NPR Weekend Edition Sunday Puzzle
July 3, 2005
Presented by Will Shortz
Puzzle by Eric Friedman

[Note from JA: I do not know how this problem was solved, as no explanation was given. This puzzle was used in the U.S. Puzzle Championship in 2005. There are two possible answers.]

A certain country mints coins in only three denominations. Each denomination is an integral number (1, 3, 4, etc.) The amounts 20, 23, and 29 can be made exactly by using three coins. What are the denominations of the coins?

Answers:

6, 7, 11 or
5, 9, 10


Friday, 29 April 2016

DAY 446

THE WOOD CHOPPING PROBLEM

Two men chopped wood all day long at exactly the same rate. The first man worked straight through without stopping to rest. At the end of the day he had a sizeable pile of logs. The second man would chop for fifty minutes and then take a ten-minute break. At the end of the day he had a much larger pile. He did not work any faster after his breaks, nor did the first man work any slower as the day wore on. How was the second man able to chop more wood?

HINT:
He did something else during his breaks other than resting.

Answer:

During each ten-minute break he sharpened his ax.

Friday, 22 April 2016

DAY 445

Credit: Nashville Banner
Red O-Donnell
In Reader's Digest
May, 1985

     The minister was pleading for funds for the church. "The Lord has done so much for you," he reminded the congregation. "You should reciprocate. Each of you here today should give a tenth of your income."  
     One member was overcome by the sermon. "A tenth isn't enough," he shouted. "Each of us should give a twentieth!" 

Monday, 4 April 2016

DAY 444

IT ALL ADDS UP
Credit: GAMES Magazine
March, 2013
Henry Dudeney

An old challenge is to get the numbers 1 through 9, in order, to form an expression that equals 100, using only basic arithmetic operations (+, -, x, div.) and parentheses. For example,

1 + 2 + 3 + 4 + 5 + 6 + 7 + (8 x 9) = 100

Can you find another solution that uses just three steps and no parentheses?

HINT:
#1: Only addition and subtraction are used.

Answer:

123 - 45 -67 + 89 = 100

Sunday, 3 April 2016

DAY 443

Starting at ONE, how high would you have to count to reach a number containing the letter A?

Answer:

One thousand

Thursday, 17 March 2016

DAY 442

THE FOUR LETTERS
Credit: GAMES Magazine
Nov/Dec 1981
Martin Gardner

A secretary types four letters to four people and addresses the four envelopes. If she inserts the letters at random, each in a different envelope, what is the probability that exactly three letters will go in the right envelopes?

Answer:

The probability is zero. If three letters match the envelopes, so will the fourth.

Wednesday, 16 March 2016

DAY 441

CAN YOU FIGURE IT?
Credit: GAMES Magazine
Sept/Oct 1981
Michael Ecker

Quickly - Is 15% of 20 the same as 20% of 15?

Answer:

Yes.......the answer to both is 3. 

Now, answer this question:

Which is larger?

94.1% of 23.25 or
23.25% of 94.1?

Answer:

They are equal - it is the same type of problem as the first example. 

A% of B will always equal B% of A, since the former equals A/100 times B (or AB/100) and the latter is BA/100.