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Friday Puzzler -- 10 in 1

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Friday Puzzler -- 10 in 1

#1

Friday Puzzler -- 10 in 1

Alex Y

This is actually ten puzzles, one for each digit.

For each digit, use that digit (and that digit only) exactly three times along with any mathematical symbols to form an expression equal to 6.

I'll take the easiest one as an example. For 2, we have a few choices:

2+2+2 =6

2+2*2 =6

2+2^2 = 6

and there is another using /, but I won't give that one here, since it is a clue to too many others ;-) .

You are not limited to the four basic arithmetic operations. For instance, sqrt is allowed, since its symbolic representation does not include a digit. However, cube root is not allowed except in a solution for the digit three, since the symbolic representation of that operator includes the digit 3.

Don't wait to get all ten--post solutions for each digit as you find them.

Re: Friday Puzzler -- 10 in 1

#2

Re: Friday Puzzler -- 10 in 1

Henry Higginbotham

More easy ones:

3!+3-3

6+6-6

6*(6/6)

Re: Friday Puzzler -- 10 in 1

#3

Good! 2,3,&6 solved


Re: Friday Puzzler -- 10 in 1

#4

Re: Friday Puzzler -- 10 in 1

Henry Higginbotham

(1+1+1)!

Re: Friday Puzzler -- 10 in 1

#5

Re: Friday Puzzler -- 10 in 1

Sam Force

5!/(5!)+5

Re: Friday Puzzler -- 10 in 1

#6

Re: Friday Puzzler -- 10 in 1

Sam Force

(8!)/8!*8

Re: Friday Puzzler -- 10 in 1

#7

Re: Friday Puzzler -- 10 in 1

Henry Higginbotham

Likewise, 7-7/7

Re: Friday Puzzler -- 10 in 1

#9

Good! 1,2,3,6 solved


Re: Friday Puzzler -- 10 in 1

#10

Good! 1,2,3,5,6 solved


Re: Friday Puzzler -- 10 in 1

#11

:-(

Alex Y

(8!)/8!*8=8, not 6

Re: Friday Puzzler -- 10 in 1

#12

Good! 1,2,3,5,6,7 solved


Re: Friday Puzzler -- 10 in 1

#14

Good! 1,2,3,5,6,7,9 solved

Alex Y

Very creative!

Another solution for 9 is

(9-sqrt(9)-sqrt(9))!

Re: Friday Puzzler -- 10 in 1

#15

Good! 0,1,2,3,5,6,7,9 solved

Alex Y

Another very creative solution!

Also, (0!+0!+0!)!

Re: Friday Puzzler -- 10 in 1

#16

Re: Friday Puzzler -- 10 in 1

Larry Barrett

4!/((sqrt4)*(sqrt4)) = 24/2*2 = 6

Re: Friday Puzzler -- 10 in 1

#17

Good! 0,1,2,3,4,5,6,7,9 solved

Alex Y

Very good!

There are lots of solutions for most of these. Another solution for 4 is

sqrt(4)+sqrt(4)+sqrt(4)

Re: Friday Puzzler -- 10 in 1

#18

Re: :-(

Sam Force

Not sure what I was thinking

Re: Friday Puzzler -- 10 in 1

#19

Re: 8

Larry Barrett

Best I can come up with is 8/(eighth root of 8 )rounded down = 8/1.2968 = 6.16 rounded down = 6.

Re: Friday Puzzler -- 10 in 1

#20

And then there were none!

Alex Y

Very good, assuming there is a mathematical symbol for "rounded down".

Here is another solution for 8:

(sqrt(8+8/8))!

Re: Friday Puzzler -- 10 in 1

#21

Speaking of symbols

Henry Higginbotham

Is there a name for the notation I used for "9"?

Re: Friday Puzzler -- 10 in 1

#22

Re: Speaking of symbols

Larry Barrett

I thought you meant 'round up' when you used the bar over the 9.

Anyway, according to google, there is a symbol for 'round down' and 'round up':

Usually, in mathematical notation we express rounding down with the floor function so ⌊ a ⌋ is the largest integer less than or equal to a. Similarly, for rounding up, we use the ceiling function, so ⌈ a ⌉ is the smallest integer greater than or equal to a.

Re: Friday Puzzler -- 10 in 1

#23

Re: Speaking of symbols

Henry Higginbotham

I've always understood it to mean that whatever part of the decimal has an overscore repeats ad infinitum. So 0.9 with an overscore on the 9 would mean 0.9999999..., or 2.485 with an overscore on the 85 would mean 2.485858585.... But I've never known what the notation is called.

I'm no mathematician, so I'd be happy to be corrected (and learn something).

Re: Friday Puzzler -- 10 in 1

#24

Re: Speaking of symbols

Alex Y

Thanks for the enlightenment, Larry!

Re: Friday Puzzler -- 10 in 1

#25

Re: Speaking of symbols

Alex Y

I agree, Henry. That is the notation I learned as well for repeating digits. But like you, I have never heard a name for the notation.

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