Unlock the Mystery of 1961 & Find a 6-Letter Perfect Word Divisible by 11

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Discussion Overview

The discussion revolves around a series of riddles and problems, including a historical reference to 1961, a logic puzzle about a password for an exclusive club, the identification of a 6-letter "Perfect Word," and finding the largest number divisible by 11 using digits 0-9. The scope includes logical reasoning, wordplay, and mathematical exploration.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • Participants discuss the significance of the year 1961, with one noting that Tottenham Hot Spurs won the double that year, suggesting it won't happen again until 6009.
  • A logic puzzle is presented where the correct response to the doorman's numbers is based on the number of letters in the words spoken, leading to various interpretations and guesses.
  • Some participants propose different answers to the password riddle, with one suggesting the answer should be "three" based on the number of letters in "ten."
  • For the largest number divisible by 11, one participant suggests 978653412 and another proposes 987645230, using the divisibility rule for 11 to justify their guesses.
  • Several participants attempt to identify a 6-letter "Perfect Word," with examples like "banter," "center," and "carter" being discussed, while noting the difficulty in finding suitable words.

Areas of Agreement / Disagreement

Participants express differing views on the answers to the riddles, particularly the logic puzzle and the largest number divisible by 11. There is no consensus on the perfect word, and multiple suggestions are made without agreement on a single answer.

Contextual Notes

Some participants acknowledge that their answers are guesses and may not be the largest or correct solutions. The discussion includes various interpretations of the riddles and the mathematical properties involved, with no definitive resolution reached.

Who May Find This Useful

Readers interested in logic puzzles, word games, and mathematical challenges may find this discussion engaging.

killerinstinct
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1. What happened in 1961 that will not happen again for over 4000 + years?

2. A man wanted to enter an exclusive club but did not know the password that was required. He waited by the door and listened. A club member knocked on the door and the doorman said, "twelve." The member replied, "six " and was let in. A second member came to the door and the doorman said, "six." The member replied, "three" and was let in. The man thought he had heard enough and walked up to the door. The doorman said ,"ten" and the man replied, "five." But he was not let in.
What should have he said?

3. PERFECT WORD is a word in which ANY one letter could be replaced by another letter to form another word. An example of a 4-letter Perfect Word is CAST because C could be replaced by L to form LAST or A by O to form COST, or S by R to form CART, and T by E to form CASE.

Give a 6-letter Perfect Word.

4.Can you find the largest number possible containing any of 9 of 10 digits, considering 0 also a number, that is divisible by 11 without a reminder?

Good LUCK! :smile:
 
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2. A man wanted to enter an exclusive club but did not know the password that was required. He waited by the door and listened. A club member knocked on the door and the doorman said, "twelve." The member replied, "six " and was let in. A second member came to the door and the doorman said, "six." The member replied, "three" and was let in. The man thought he had heard enough and walked up to the door. The doorman said ,"ten" and the man replied, "five." But he was not let in.
What should have he said?
i can only solve this one, i don't know about the others...<<<<< SMILIES >>>>>

Is it 3 and the last one will say 1.5 ? :-p

-Ali.and.the.40.thieves,
 
Is that a guess or is there a logical reason for giving the solution??
 
how can you say it is a guess ? I tried to think and computed as correctly as i could...
12/2=6
6/2=3
3/2=1.5
Thats a Logical reason ?
 
If dividing by 2 is your logical response. Then if the guard said 10, then you should have replied 5. But that is not the case, as written in the question. This question is not as simple as just simply dividing by two!
 
killerinstinct said:
2. A man wanted to enter an exclusive club but did not know the password that was required. He waited by the door and listened. A club member knocked on the door and the doorman said, "twelve." The member replied, "six " and was let in. A second member came to the door and the doorman said, "six." The member replied, "three" and was let in. The man thought he had heard enough and walked up to the door. The doorman said ,"ten" and the man replied, "five." But he was not let in.
What should have he said?

the word twelve has 6 letters
the word six has 3 letters
the word ten has 3 letters

he said 5 and was not let in, so he should have tried saying 3 instead,
maybe that would have worked

I like these riddles, thank to K.I. for posting them
 
oh well, :-p
 
marcus is correct! The answer to the doorman's numbers was the number of letters in the word he said. There are still 3 more unsolved questions, good luck!
 
killerinstinct said:
4.Can you find the largest number possible containing any of 9 of 10 digits, considering 0 also a number, that is divisible by 11 without a reminder?

Good LUCK! :smile:

K.I. here is just a guess, I didn't check it to see if it is the largest
but only that it is fairly large, and it uses each of the digits from one to nine exactly once, and it is divisible by 11


978653412

I didnt use a computer, someone who wants to write a short program in basic computer language could quickly find out what is the largest
 
  • #10
1. Tottenham Hot Spurs won the double in 1961, they won't win it again 'til 6009 (i.e when the last two digits of the year are first 2 upside-down)
 
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  • #11
marcus said:
K.I. here is just a guess, I didn't check it to see if it is the largest
but only that it is fairly large, and it uses each of the digits from one to nine exactly once, and it is divisible by 11


978653412

I didnt use a computer, someone who wants to write a short program in basic computer language could quickly find out what is the largest

I reckon it's 987645230.

I guessed this using the test for divisibilty for 11 i.e.

9-8+7-6+4-5+2-3+0 = 0
 
  • #12
Canter:

banter
center
carter
cancer
cantor
canted

Thinking of a 6-letter perfect word was hard as (to me anyway) there are no obvious ones and there are words like 'hanger' in which all the letters but one can be replaced.
 
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  • #13
jcsd said:
I reckon it's 987645230.

I guessed this using the test for divisibilty for 11 i.e.

9-8+7-6+4-5+2-3+0 = 0

Actually I'm being silly, you can get eveb bigger numbers using the test

e.g. 987652413

as:

9-8+7-6+5-2+4-1+3 = 11

A quick test confirm that 987652413 is the highest such number.
 
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  • #14
Wow, it seems like all the riddles are solved. Good Job all!
 

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