hmm, I thought that this was a simple one, but turns out it isn’t as straightforward as I thought it was.
5/27
Summary...maybe?...nevermind this is wrong...
It’s just (n-1)! = 4! = 24 innit?
There are 4 ways the first cup could be placed, but then there are four or three ways the second cup could be placed, if the first cup is on the color of the second, then three or two, then two or one and finally one - so I don’t think it is that obvious
Ahhh, yes. That’s correct. I’ll come back to it after lunch if it isn’t figured out by then…
5/27
- Proof by Exhaustive Search
Summary
I was thinking 115 ---- 5! - 5 (the own color options)
DeepPurple is correct!
Here's the reasoning given
Let’s call the five cup/saucer colors A, B, C, D, and E. You have four choices of cups (B, C, D, or E) to place on saucer A. Next, put cup A on the saucer that matches the cup on saucer A (so if you chose cup C on saucer A, put cup A on saucer C). There are two choices for placing a cup on the next open saucer (for example, you could place D or E on B), but after that the remaining cups are decided so as not to have any matching pairs. There are 4x2=8 ways to arrange the cups and saucers if you mirror the first cup/saucer combo with the second choice.
Suppose instead you don’t do that. You have four choices of cups (B, C, D, or E) to place on saucer A. Suppose, for example, that you choose cup B to put on saucer A. Then on saucer B, you have three choices of cups (C, D, or E) since you’re not going to use A yet. Suppose you choose C. Then on saucer C, there are three choices of cups (A, D, or E). But once you’ve chosen that cup, the positions of the other two are determined since you can’t match a cup and saucer with the same color. There are 4x3x3=36 ways to arrange the cups if you don’t mirror the first cup/saucer combo with the second choice. In all, there are 8+36=44 different arrangements of unmatched cups and saucers.
Well, that was a fun one.
5/28/2021 - OPPOSING CHANGE
Change one letter in both words in each row to create a pair of antonyms or counterparts. For example, OVEN and CLOSET becomes OPEN and CLOSED. Can you solve them all?
- COOLISH WIDE
- DILATE THICKET
- CONGEAL SHOP
- RAMS NICHES
- NEAT FUR
- BLOND RIGHTED
Summary
- FOOLISH WISE
- DILUTE THICKEN
- CONCEAL SHOW
- RAGS RICHES
- NEAR FAR
- BLIND SIGHTED
Dang you’re fast!
I was able to get all of them except #4. Was working on that one when you posted.
Last one for today.
5/29/2021 - AT THE MOVIES
I’m sitting on one of the seats in a movie theater. There are 14 more rows of seats behind my row than in front of my row. Also, there are 3 times as many rows of seats behind my row as in front of my row. If each row contains 30 seats, how many seats are there in total in the theater.
5/30/2021 - CHANGING JOBS
Pair up each three-letter word with a four-letter word and rearrange the seven letters together to form an occupation. Each word is used only once. What are the four jobs?
3 letter words 4 letter words TAU CURB SIR TEST DIN RACY THE LOFT
5/29
Summary
There are 870 seats. Seven rows in front of him, 21 rows behind him, plus his row gives you 29 rows. Multiply by 30 seats per row to get 870 seats.
That is correct! I don’t think I’m going to be able to figure out the 5/30 puzzle though.
Summary 5/30
Actuary
Florist
Dentist
Butcher
I’m a little annoyed at myself that I couldn’t figure out that top one you have listed!!
Summary
I started with racy, because I thought it would be easiest to identify a profession with y in it, and then laughed because it turned out to be ours.
Never heard of ASPIC
Love one of the occupations! Amazing.
I got that one early on in that puzzle. I have heard of aspic before, although the thought of meat flavored jello is kinda gross, imho.