Puzzles
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Alice is visiting the Maths section of her local library. She takes a large old book from the shelf and sits down at a desk to read. The book falls open somewhere in the middle. Alice is initially disappointed to see that the left hand and right hand page numbers are not consecutive – there are a number of pages missing. But Alice is delighted to note that, read left to right, the digits of the two page numbers form a consecutive descending sequence of digits. What is the minimum number of pages that could be missing from the book?
The page numbers in the original book start at one and each page is numbered sequentially.
[I really like this puzzle, thank you! Harry]
A very nice puzzle Rhydwen! Would the answer be 7, leaving page 2 next to page 10?
89246: 22
@Rhydwen23
We must have that both page numbers are of opposite parity (oddness/evenness) since one is a left page and one is a right page. Because of this the rightmost page must have an odd number of digits, so the smallest solution is 43/210 with 83 pages (front and back) missing. If you like your left pages even, the smallest solution is 54/321 with 133 pages missing.
@Rincewind, if you consider the page number on the missing leaves you may see a problem with this solution.
I agree with Tildy I think its 22
Response to Three Gods
For the three gods, I would ask A “What would you say if I asked you if you were the truth-teller and or the god of falseness” If they say yes then I know they must be one or the other, so I would ask B ‘what would you say if I asked you if are the god of truth’ and if they say yes I I know they must be telling the truth so the last one would be randomness and if they say no then I would ask the last a similar question about the god of falseness. But if they say no after the first question, then I would know they are the god of randomness and test for the last two Gods in similar ways as I would in the first scenario.
Regarding #89246
Well done @kford_academy.
Each missing leaf has two sides and carries two pages.
The left and right pages of the open book, even with pages missing, are either left odd and right even, or left even and right odd.
The number of the right hand page is always greater than the number of the left hand page.
Any combination of single digits are out because the missing leaves each have two sides, so the remaining single digit numbers cannot be consecutive.
Looking a one and two digit sequences…
The sequence of 2 and 10 is out because both numbers are even.
The sequence of 3 and 21 is out because both numbers are odd.
Similar for 4, 32; 5, 43; 6, 54; 7, 65; 8, 76; 9, 87.
Any combination of two and two digit sequences is out because the left-hand page number needs to be higher than the right-hand page number.
The sequence 3 and 210 (206 pages, 103 leaves missing) is an obvious candidate, being a combination of odd and even numbers.
As is 54 and 321 (266 pages, 133 leaves missing).
I believe the best solution is 43 and 210 (166 pages, 83 leaves missing).ANSWER Left page 43. Right page 210. Combined sequence 43210. Difference between pages 167. 166 pages missing, or 83 leaves (pages front and back).
Response to the Three Gods
I was first introduced to the puzzle years ago on Ted-Ed. However my interpretation is fairly different from what I remember from that time as I have learnt more about logic.
The most simplest form is to ask the question, “Is sound x (let’s say, ba, for example), yes.” If it is true, the answer given must be yes, ba. No will result in the same as no is ba. The inverse is also true, if asking is ba no, however fa will always be the answer.
The previous response is totally correct but this logic is key to getting actual answers whilst deducting their nature. This is more optimal, and provides a solution in three because no translation is required.
I would have liked to try and reconcile the two but this is already long and the last time I wrote this I was accidentally logged out.
I really hope I don’t get scooped.An Ordinary clock has two hands, with the larger hand moving faster around the face of the clock.
Assuming the clock keeps perfect time, how many times will the long and short hands pass over each other between 12 noon and Midnight.
Ask God A ” Are you speaking the truth ? ” . The answer will be yes no matter the god. Now i know da or ja is yes. Now I ask god B if God A is the truth god. If it is yes, then it is the random god. I dont know afterwards…
Alright, so this is a riddle I heard once, but I can’t remember where from, so it’s not exactly my own, but I thought people may enjoy it. It’s pretty simple, once you figure it out.
I call it: The Elite Club
You’re on the trail of a murderer, and you follow their tracks to a place called the Elite Club. You notice that there’s a bouncer outside, and the members go up and talk to the bouncer before entering. You decide to get close to listen.
The first member approaches the bouncer, and the bouncer says “Six”. In response, the member says “Three”, and is admitted into the club.
A little while later, another member arrives. To this one, the bouncer says “Twelve”. The member replies “Six”, and is also let in.
Suddenly, a man who clearly doesn’t belong approaches the bouncer. The bouncer, after a sideways glance, says “Four”, to which the man confidently replies “Two”.
The bouncer chases the man off, meaning he got it wrong.What is the secret behind the password?
@Luke-Chesters:
You say ‘Five’.
I say […].You say ‘Fourteen’.
I say […]Hi,
I think that the good answer is “four”.
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