BMAD

stirk

Suppose you have one square tile of each of these side lengths: 1, 4, 7, 8, 9, 10, 14, 15, and 18 feet. How can you fit them together into a rectangle? (With no cutting or overlapping, of course.)

We are still missing the most optimal solution for (ii).

I have you slightly off.

sorry but 1 is what i was looking for.

very very close. and welcome!

correct answers

well explained!

In the picture, assume the gears have 15, 16, and 17 teeth from left to right. Number each gear clockwise, 0-14 0-15, 0-16, with (0, 0, 0) at the top at noon. Assuming the gears take exactly one second per tooth, answer these: What do the numbers say at 12:34 a.m.?

Every male bee has just a female parent, while every female bee has both a male and a female parent. How many ancestors does a male bee have, counting twenty generations? Note: Don't count this male as a generation or include him in the 'final tally.'

That 'Math Council Dinner' is in December, but I forgot which night, so I asked around. Alan said that the date was an odd number; Brenda claimed it was greater than 13. Carly declared it was not a perfect square, while Dara swore it was a perfect cube. Finally, Edward told me the date was less than one-fourth his age, which I know to be 68. Yesterday I learned that only one of them had told the truth! What is the date of the dinner?

The first funny number: If a 1 is placed after this five-digit number, the result is triple the number you'd get by putting the 1 in front. The second funny number: It's the second-smallest odd number greater than 1 that's a perfect cube and also a perfect square. The third funny number is the smallest with the property that if any prime between 10 and 20 is divided into it, the remainder is 1. What's the exact product of the three funny numbers?

Yes, I guess. Maybe it is because english isn't my native language...but if i was at a party and make a question in the third person, usually the person named wouldn't answer this. For example: if sara and Diana are standing next to each other and I say.... Does Sara like pets?, it would seem awkward for Sara to answer. Sure. There is a person named Sylvia. That person has a truth property: Sylvia(Truthful) or Sylvia(Liar). Any person knowledgable on the subject, (that includes Sylvia) can respond to the question: Sylvia(Liar)? I was uncertain about these: "Aren't you Sylvia?" Do you say yes or no truthfully if you are? "Are you twins?" And "are you Mia?" Don't seem to resolve it. "Sylvia, want this?" Might decompose to "are you Sylvia AND if so do you want this?" Which the sister could respond to.

BGM's answer makes sense but I disagree that the title was critiqued

Would Sylvia respond to this question?

This solution is quite similar

we don't know if Sylvia tells the truth

Stirs

yes. And the solution changes if the road is straight as in the other problem

I believe this question is a classic but I am unable to find it in the forums so I will venture the wrath of the moderator gods by posting it anyways: "Only the smartest one shall survive," said the executioner. "All of you prisoners will be seated around this round table. I will chop off the head of the prisoner in seat #1, skip seat #2, chop #3, etc. Beheaded bodies (and chairs) will be cleared away post haste. When I get to the end I will continue to chop, skip, chop, until there is but one prisoner remaining, who will then be freed." a) If there are 13 prisoners, which is the lucky seat number? b) In the morning, you will be told how many prisoners, n. You must figure out the best seat quickly, just knowing n. Which seat, k, should you 'head' for, in order to be freed?

Much closer but there is still an even shorter path.