Daily Challenges

[Peckris 2]

8 minutes ago, Paddy said:

... One of each.

On the first run through if any student can see four stamps the same colour they would know immediately that their own must both be the opposite colour. So each must be seeing at least one student with opposite colour stamps.

On the second run, the first student cannot be sure if his stamps are the same colour yet, so cannot answer. By the second student the only possibility remaining is that his stamps are opposite colours, otherwise the first student would have had the answer.

(I think!)

 

I agree.

I think each of the students sees one of each on the other two foreheads. If the first (A) saw two the same on one forehead, then one of the other two (B or C) would see the same and would know from A's first reply that he can't see 4 the same. So B knows from A's second reply that each person sees one of each on all of them, and therefore he knows there is one of each on his own. (A bit convoluted but I know what I mean!)

[DaveG38]

You are all correct that it is a green and red stamp, but the logic that leads to this is quite extensive. As a starting point, if the first student sees 4 red stamps on the other two students foreheads then he knows immediately that he has 2 green on his own. And vice versa if he sees two green. Hence if he says he doesn't know this can't be the solution. This conclusion is one that the next student understands so he then goes through all the possible combinations to conclude that he doesn't know either, and so on. Each successive question to a student results in the student analysing what the previous student(s) concluded, and taking the problem forwards. By the time we get to the fifth round, the student has examined all the previous possibilities and knows that these can all be discounted, and so he comes to his own definitive conclusion - one red and one green.

I could go through each stage with all the permutations and the conclusions drawn, but there aren't enough hours in the day to do this. Try it if you want to, but it takes many pages of 'what ifs' to get to the answer. 

   

[Sword]

I tried to write out all the permutations and eliminate. All the RR or GG for student 2 have been eliminated and so I would make it RG for student 2. 

 

RR RR GG GG

RR RG RG GG

RR RG GG RG

RR GG RR GG

RR GG RG RG

RR GG GG RR

 

RG RR RG GG

RG RR GG RG

RG RG RR GG

RG RG RG RG

RG RG GG RR

RG GG RR RG

RG GG RG RR

 

GG RR RR GG

GG RR RG RG

GG RR GG RR

GG RG RR RG

GG RG RG RR

GG GG RR RR

[DaveG38]

11 hours ago, Sword said:

I tried to write out all the permutations and eliminate. All the RR or GG for student 2 have been eliminated and so I would make it RG for student 2. 

 

RR RR GG GG

RR RG RG GG

RR RG GG RG

RR GG RR GG

RR GG RG RG

RR GG GG RR

 

RG RR RG GG

RG RR GG RG

RG RG RR GG

RG RG RG RG

RG RG GG RR

RG GG RR RG

RG GG RG RR

 

GG RR RR GG

GG RR RG RG

GG RR GG RR

GG RG RR RG

GG RG RG RR

GG GG RR RR

Well done that man!

[Sword]

Thanks! I enjoyed doing that.

[1949threepence]

1/ What common English verb becomes its own past tense by rearranging its letters? SOLVED

2/ It occurs once in a minute, twice in a moment, but never in an hour. SOLVED

3/ A cowboy rides into town on Monday. He stays three days, then rides out of town on Monday. How?

4/ How was the October record set in March?

Edited April 8, 2020 by 1949threepence

[Sword]

6 minutes ago, 1949threepence said:

2/ It occurs once in a minute, twice in a moment, but never in an hour.

The letter m

[Sword]

13 minutes ago, 1949threepence said:

1/ What common English verb becomes its own past tense by rearranging its letters?

eat and past tense is ate

Edited April 8, 2020 by Sword

[mrbadexample]

3. Monday is his horse.

 

[1949threepence]

10 hours ago, 1949threepence said:

1/ What common English verb becomes its own past tense by rearranging its letters? SOLVED

2/ It occurs once in a minute, twice in a moment, but never in an hour. SOLVED

3/ A cowboy rides into town on Monday. He stays three days, then rides out of town on Monday. How?  SOLVED

4/ How was the October record set in March?

No 4 anybody?

[Sword]

9 minutes ago, 1949threepence said:

No 4 anybody?

I thought "March" could be referring to the town of March. But I don't what the record refers to.

[Rob]

Rainfall?

[1949threepence]

Temperature - the (then) October maximum temperature record was broken in March (Cambs) on 1st October 1985, when 29.4 degrees was attained there. This was broken on 1st October 2011, when 29.9 degrees was reached in Gravesend.

[Chingford]

1 hour ago, Sword said:

I thought "March" could be referring to the town of March. But I don't what the record refers to.

 

33 minutes ago, Rob said:

Rainfall?

Temperature, highest October on record, recorded in March, Cambridgeshire,

[Paddy]

A few word puzzles for some brief diversion. All answers are in the English dictionary and cannot be hyphenated:

1. What is the longest word that can be typed on the top letter row of a UK keyboard?

2. What is the longest word with no tall letters (above the line like l, or below like g)? (All lower case.)

3. What is the longest word with ALL tall letters?

4. What words contain all the vowels just once each in alphabetical order? (Two answers.)

5. Which word contains the most consonants in a row?

6. Which word has the most vowels in a row?

7. What word contains the letters WKW together in that order?

8. I think there is a word that contains all the vowels just once each in reverse order, but I can't remember it!

Some easier than others!

 

 

 

[Rob]

Try syzygy for most consonants?

[Paddy]

28 minutes ago, Rob said:

Try syzygy for most consonants?

My answer also has 6, but doesn't use the debatable "y".

 

Edited April 9, 2020 by Paddy
Correction

[mrbadexample]

1. Typewriter.

[mrbadexample]

4. Abstemious, facetious.

[mrbadexample]

6. Euouae?

[mrbadexample]

7. Hawkwind.

 

Also awkward.

Edited April 9, 2020 by mrbadexample

[mrbadexample]

5. Strychnine must be close?

[Paddy]

2 hours ago, Paddy said:

A few word puzzles for some brief diversion. All answers are in the English dictionary and cannot be hyphenated:

1. What is the longest word that can be typed on the top letter row of a UK keyboard? - Typewriter

2. What is the longest word with no tall letters (above the line like l, or below like g)? (All lower case.)

3. What is the longest word with ALL tall letters?

4. What words contain all the vowels just once each in alphabetical order? (Two answers.) - Abstemious, Facetious

5. Which word contains the most consonants in a row?

6. Which word has the most vowels in a row?

7. What word contains the letters WKW together in that order?

8. I think there is a word that contains all the vowels just once each in reverse order, but I can't remember it!

Some easier than others!

 

 

 

Two definitely correct with the answers I had in mind as shown.

Not sure about Euouae - it is an abbreviation and often written with Vs instead of Us, so I think is borderline. (Although I know you get away with it ins Scrabble.) My answer has 5 vowels in a common everyday word.

Hawkwind is not in the dictionary as it is a band name.

I like the idea of Strychnine as an answer, although it does use the disputable Y, which is used as a vowel. My answer has 6 consonants without using a Y.

[1949threepence]

No 3 - the best three I can come up with so far are "unreasonableness", "declassification" and "discontentedness", all with 16. They are in the dictionary.

That's obviously using just lower case.

There's probably longer better ones.

[Paddy]

1 hour ago, 1949threepence said:

No 3 - the best three I can come up with so far are "unreasonableness", "declassification" and "discontentedness", all with 16. They are in the dictionary.

That's obviously using just lower case.

There's probably longer better ones.

That's not answering the need to be all tall letters - tall letters are b, d, f, g, h, j. k. l, p, q, t, y.