Daily Brain Puzzlers Calendar

The Sandbox Games
1005

7/28/2021
Kendrick has six knickknacks which are identical except that three are silver and three are gold. Kendrick wants to place them in a row on the shelf so that each silver knickknack is next to at least one gold knickknack. How many different color arrangements are possible?

1006
7/28?

6?

gsgsgs
gssgsg
gssggs
sgsgsg
sggsgs
sggssg

1007

not quite. You are still missing some possibilities.

1008

I get 10

Summary

G S G G S S
G S G S G S
G S G S S G
G S S G G S
G S S G S G
S G G S G S
S G G S S G
S G S G G S
S G S G S G
S S G G S G

1009

That is correct!

ETA: the total number is correct, 2 of those combinations are incorrect but can be replaced with missing correct ones.

1010

Your first and last combinations donā€™t look right.

1011

Here are the official combinations:

7/28

5 arrangements can start with Silver

  • S G G S G S
  • S G G S S G
  • S G S S G G
  • S G S G S G
  • S G S G G S

Then 5 more starting with Gold

  • G S G S G S
  • G S G S S G
  • G S S G G S
  • G S S G S G
  • G G S S G S
1012

I agree - they donā€™t have a G next to each S.

1013

seemed too easy, but then there were work things.

1014

Yeah, small mistake. I actually did this in 1ā€™s and 0ā€™s.

First, I calculated that there were 2^6 = 64 combinations of gold and silver, ignoring the 3 count of each at this step.

I calculated each number from 1 to 64 in binary. Then I eliminated all the numbers whose sum-of-digits did not equal 3. That left 20 numbers. I manually checked the 20 and found 10 that met the questionā€™s criteria. Then I changed the 1ā€™s and 0ā€™s into Sā€™s and Gā€™s. I should have changed them to Gā€™s and Sā€™s.

The last combinatorics question I also did an exhaustive search to solve.

1015

Thatā€™s a smart way to do it

1016

Neat approach!

1017

Sorry, that should have read that I calculated the numbers 0 to 63 in binary.

1018

I figured from the two you were missing compared to the two that you had put that it was just a typo.

1019

And now, for the first time, the actual puzzle for today!

7/29/2021 - PUTTING UP A FRONT
In each row, find a four-letter word that can go before each of the four words to form four common compound words or phrases. Can you do it in one, two, three, or four clues? To prevent looking ahead, the 2nd, 3rd, and 4th words of each set are in spoilers.

Set 1: Word 1: HOUSE
Word 2. SHIP
Word 3. CRIER

Word 4. HALL

Set 2: Word 1: LETTER
Word 2. BIRD
Word 3. HANDLES

Word 4. AFFAIR

Set 3: Word 1: BALL
Word 2. GAME
Word 3. GROUND

Word 4. HAIRED

Set 4: Word 1: LAND
Word 2. FRAME
Word 3. DRAG

Word 4. STAY

1020

I can honestly say I didnā€™t get any of theseā€¦ and Iā€™m not sure I would have if I had taken more time on them either. I kind of have to do this one as I type it out since I have to read all of the words as I type them, so I donā€™t give myself too much time for any one word. Then I looked at the answers because after reading all the words I still couldnā€™t figure it out :laughing:

And for some reason the third word of the first set was really hard for me to figure out what it said when it was written backwards: REIRC

1021

7/29

Summary

Set 1: TOWN (guessed after word 3)
Set 2: LOVE (guessed after word 1)
Set 3: FAIR? (guessed after word 4)
Set 4: No idea, even after four words

1022

You are correct on the first 3! Weā€™ll see if someone else can get #4.

1023

I will say for that fourth one I donā€™t think the third word ā€œdragā€ fits the word as well as the other three. Itā€™s a word/term Iā€™m not familiar with.

1024

2 is the only one I got