BrainDen.com - Brain Teasers

# bonanova

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1. ## One Blind Man

Yes. The restriction is only that they can't read each others' labels.

3. ## One Blind Man

Four identical boxes, each box containing 3 balls, each ball being either black or white, were placed before four men: Al, Bert, Cal and Don. No two boxes contained the same selection of ball colors. Each box bore a label that correctly identified the contents of one and only one of the boxes, but no individual box bore its correct label. After each man, at random, was given one of the boxes, they were given the following test. Each in turn, and out of sight of the others, was to blindly remove two of the balls from his box, read the label on his box, and then endeavor to tell to the others the color of the third ball, which remained in the box. It did not seem a difficult task, but the results were a bit surprising: Al: I've drawn two black balls. I can tell you the color of the third ball. Bert: I've drawn one white ball and one black ball. I can tell you the color of the third ball. Cal: I've drawn two white balls. I'm not able to tell you the color of the third ball. Don: (who was blind, and could not read his box's label) I don't need to draw. I can tell you the colors of the balls in my box. I can tell you the color of the third ball in each of the others' boxes. And then he proceeded to do so. How did he tell?

5. ## Alphabet baseball

You're right. Nice solve.
6. ## Alphaplication

You can eliminate the second case else there would be another X in the puzzle statement. Nicely done.
7. ## Who's keeping score?

Didn’t all break ... just rules out the case that all broke ... anything else is possible Between Ed and Jim means beat one and lost to the other. I have somewhat different answer.
8. ## Alphabet baseball

Ok what I was looking for is that if no one called their initial then they must have alternated teams when they formed the circle. So that fact didn’t need to be given as a separate condition or assumed. Initials occurring in odd positions of the alphabet must have held even positions in the circle.
9. ## Alphaplication

Sharpen your pencil for this one. Each period is a missing digit. . . . X . ======= X . . Y . X Y ------- . Y X Y What two numbers are being multiplied?
10. ## Who's keeping score?

When four friends, Bill, Ed, Jim and Tom, began their foursome at Fairview Links last Saturday, they discovered to their dismay that no one had brought a pencil to keep their scores. And well let's just say that in the clubhouse afterward there was some confusion. Here are four "facts" that each player remembered. But fair warning, it turns out only two of each group of statements are true. And, if it helps, they all correctly remembered that no two players had the same final score. Bill: I beat Jim and Tom. Ed shot 111. Jim took 6 on the last hole. None of us broke 100. Ed: Bill wasn't last. I was the winner. Jim finally broke 100. I shot 98. Jim: I beat Bill and Ed. The last hole was not my best. We didn't all break 100. Tom wasn't the winner. Tom: Ed beat Bill. I was the winner. Bill placed between Ed and Jim. The last hole was Jim's best. That's it. But surely by now you know what order they actually placed.
11. ## Ten Islands

In a dream I visited a city named Ten Islands, a charming archipelago connected by a system of bridges, five of which led to the mainland. Four of the islands were serviced by four bridges, three others by three bridges and two others by two bridges. The final island could be reached by only one bridge. The city was well laid out, and the view from each of the bridges provided a new and enchanting visual experience. I shared the dream later with my son, remarking again and again of the city's beauty. Even if you hadn't mentioned the fact to me, Dad, I would have told you this was not a real experience, he replied. Ten Islands, as you described it, could not exist in this world, only in a dream. How could he be certain of that?

With discussion help from @plasmid, here is a 9-crumb solution. Kudos again for an engaging puzzle. Path A 1 2 C Path C 3 E Path E 4 B D
13. ## Alphabet baseball

I asked the players about that last night. Jenkins, Babcock and Morris recalled they were not standing next to a team mate; then several others said the same. Smith and Peters agreed, but added that they were quite certain they weren't told to alternate, noting the process was supposed to make home team selection a random process. They all agreed that it might have happened by chance.

What precludes the mouse from going from G(2) to G(5)? (My eyes are getting bleary ...)

I think there's a proof for the pentagon case.

This was a fun puzzle.

Kudos to the pretty girl in the green dress.
18. ## Why we're all in debt

@plasmid was discussing finances with his planner the other day. After they reviewed tax returns and year's worth of receipts, the advice he received was just this: S P E N D - L E S S ========= M O N E Y You's think so, he replied, but I've determined that this is quite impossible. Is he right?

I understand that the mouse goes to the nearest crumb, and that "nearest" means shortest euclidean (straight line) distance. So (haven't read the spoiler yet) I never conceived the mouse would get advantage by doing otherwise. I'm assuming the mouse is playing strictly according to his own hunger advantage. Am I right about that? Oh wait. you're saying that Give me a day or two to work on that?

@CaptainEd @plasmid

@plasmid Interesting puzzle and thanks for the call out. EDIT: Thought this was optimal, but now have read @CaptainEd's solution. Tip of the cap, Nice going. FWIW, my best efforts follow .... Breadcrumbs (red circles) are placed at the five vertices A B C D and E. Object is for our mouse to take four straight paths: AC, CE, EB, and BD. Because we have a greedy mouse that goes to the nearest snack, it will move from a vertex to an adjacent vertex whenever it has an uneaten crumb. That must be prevented. So we draw inter-vertex-radius circles -- a red circle centered on A, a green circle centered on C and a blue circle centered on E -- to help define advantageous areas to place our minimum (M) count of additional tasty crumbs to keep our mouse on its intended path. It is quickly evident that M can't be less than 5. (First-pass solution.) Second-pass solution.
22. ## Lunch Games

At lunch yesterday four students, Al, Bill, Jack and Tom (last names Conner, Morgan, Smith and Wells, in some order) amused themselves by dealing poker hands to all, with the winner being the holder of the best hand. The winner of the first hand was to collect 10 cents from the other three; the second-game winner would collect 20 cents each; the third winner get 30 cents each; and so on. When the bell rang for afternoon classes to begin, four hands had been dealt, with each student winning once, in this order: Jack, Morgan, Bill and Smith. At the outset Tom had the most money, but at the end Wells had the most. What are the students' full names?
23. ## Alphametic

OK these subtractions do not work using letters. But make a number substitution, the same for both, and everything's fine. N I N E N I N E - T E N - O N E ======= ======= T W O A L L
24. ## Alphabet baseball

The local Literary Society had just enough members to field two teams, and so they decided one Saturday in June to play a baseball game down at the park. After members were assigned to teams, aptly named the Prose and the Cons, they purposed to determine which team would be the home team in a sort-of literary manner. The 18 players formed a circle and began counting, clockwise, using the letters of the alphabet rather than numbers. It was decided that if the "count" ever got to "Z" the next player would continue by calling out "A" and so on. The process would continue until a player named the letter that was also his initial. That player would then gain the honor of having his team bat last. The captain of the Cons went first, calling out "A", the next player called "B", and so it went. Surprisingly, after 360 letters were called no player had called his initial. Well, said one, it was a nice thought, but hey let's just flip a coin, already. And thus the Prose were named home team. But by then it was dark, and the game was accordingly postponed until the following weekend. But when they gathered next to play, there was a disagreement about who was on which team, owing to the fact that no one had bothered to write the rosters down. No problem, though. All 18 members of the Lit Soc, Taylor, Brown, Jenkins, Miller, Gerson, Babcock, Adams, Randolph, Carver, Smith, Flynn, Sawyer, Timmons, Myers, Lucas, Morton, Young and Peters, were also long time members of BrainDen and thus had no difficulty at all in reconstructing the team rosters. And neither should you. Who played for each team?