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Ways to make six
Posted: January 31st, 2024, 10:58 am
by Rover110
This has been set as the "challenge of the week" at my son's school.
Insert mathematical symbols (no digits) to make each calculation equal six. You can use ANY mathematical symbol you like so think carefully.
2 2 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6
Spoiler:
I don't think my son has learned about cube roots, or if they're allowed. But that's the way I thought for doing 8
Re: Ways to make six
Posted: January 31st, 2024, 3:29 pm
by UncleEbenezer
What's your definition of "ANY mathematical symbol"? Have dodgy spreadsheet functions made their way into that lexicon, 'cos it's the first way I can see to do 8 (I know no way to express your spoiler that doesn't involve introducing a digit in the notation).
(2,3,5,6,7 trivial; 4 and 9 each one step from 2,3).
Re: Ways to make six
Posted: January 31st, 2024, 5:02 pm
by XFool
Secondary school maths I can do!
Rover110 wrote: 8 8 8 = 6
Spoiler:
I don't think my son has learned about cube roots, or if they're allowed. But that's the way I thought for doing 8
Spoiler:
......................... 8 - SQR(SQR(8 + 8)) = 6I don't know what is going on with the display here!
Re: Ways to make six
Posted: January 31st, 2024, 7:09 pm
by tjh290633
UncleEbenezer wrote:What's your definition of "ANY mathematical symbol"? Have dodgy spreadsheet functions made their way into that lexicon, 'cos it's the first way I can see to do 8 (I know no way to express your spoiler that doesn't involve introducing a digit in the notation).
(2,3,5,6,7 trivial; 4 and 9 each one step from 2,3).
It looks simple to me. Cube root of 8 + ditto + ditto.
TJH
Re: Ways to make six
Posted: January 31st, 2024, 7:23 pm
by UncleEbenezer
tjh290633 wrote:UncleEbenezer wrote:What's your definition of "ANY mathematical symbol"? Have dodgy spreadsheet functions made their way into that lexicon, 'cos it's the first way I can see to do 8 (I know no way to express your spoiler that doesn't involve introducing a digit in the notation).
(2,3,5,6,7 trivial; 4 and 9 each one step from 2,3).
It looks simple to me. Cube root of 8 + ditto + ditto.
TJH
The rules said no digits. The cube root sign requires the digit 3 to distinguish it from other roots.
But a solution that doesn't rely either on digits or a horrible spreadsheet hack has now been posted.
Re: Ways to make six
Posted: January 31st, 2024, 8:23 pm
by mc2fool
UncleEbenezer wrote:tjh290633 wrote:It looks simple to me. Cube root of 8 + ditto + ditto.
TJH
The rules said no digits. The cube root sign requires the digit 3 to distinguish it from other roots.
Cube root was also sort of excluded in the spoiler in the OP.
UncleEbenezer wrote:But a solution that doesn't rely either on digits or a horrible spreadsheet hack has now been posted.
And here's another:
Sqrt(8 + (8/8))! = 6 
Re: Ways to make six
Posted: February 1st, 2024, 6:07 pm
by 9873210
There are multiple "universal" answers.
A simple one is to add the digits and then tack on as many copies of "± π/π" as needed.
Or more explicitly for all digits n != 0
nn/n - π/π - π/π - π/π
Re: Ways to make six
Posted: February 1st, 2024, 6:23 pm
by 9873210
9873210 wrote:
There are multiple "universal" answers.
A simple one is to add the digits and then tack on as many copies of "± π/π" as needed.
Or more explicitly for all digits n != 0
nn/n - π/π - π/π - π/π - π/π - π/π
Won't let me edit original