100 using only 5 number of digits

Clash Royale CLAN TAG#URR8PPP

up vote
1
down vote

favorite

I have a problem from Martin Gardner I can’t solve. Please help!

For each digit $1leq dleq 9$, make 100 using exactly five number of $i$s. Any operation is allowed, brackets as well.

For $i=1,2$ I have a solution:

$$100=111-11$$

$$100=(2*2*2+2)^2$$

For the rest please help.

number-theory

share|improve this question

edited 1 hour ago

jafe

7,5861885

asked 1 hour ago

Pet123

61

New contributor

Pet123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  In case anyone missed it, the same problem with exactly 6 /i/s is trivial: (iii - ii) / i works for any i in any base > i.
  – Rupert Morrish
  32 mins ago
  

  
  
  
  

add a comment | 

up vote
1
down vote

favorite

I have a problem from Martin Gardner I can’t solve. Please help!

For each digit $1leq dleq 9$, make 100 using exactly five number of $i$s. Any operation is allowed, brackets as well.

For $i=1,2$ I have a solution:

$$100=111-11$$

$$100=(2*2*2+2)^2$$

For the rest please help.

number-theory

share|improve this question

edited 1 hour ago

jafe

7,5861885

asked 1 hour ago

Pet123

61

New contributor

Pet123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  In case anyone missed it, the same problem with exactly 6 /i/s is trivial: (iii - ii) / i works for any i in any base > i.
  – Rupert Morrish
  32 mins ago
  

  
  
  
  

add a comment | 

up vote
1
down vote

favorite

up vote
1
down vote

favorite

I have a problem from Martin Gardner I can’t solve. Please help!

For each digit $1leq dleq 9$, make 100 using exactly five number of $i$s. Any operation is allowed, brackets as well.

For $i=1,2$ I have a solution:

$$100=111-11$$

$$100=(2*2*2+2)^2$$

For the rest please help.

number-theory

share|improve this question

edited 1 hour ago

jafe

7,5861885

asked 1 hour ago

Pet123

61

New contributor

Pet123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

I have a problem from Martin Gardner I can’t solve. Please help!

For each digit $1leq dleq 9$, make 100 using exactly five number of $i$s. Any operation is allowed, brackets as well.

For $i=1,2$ I have a solution:

$$100=111-11$$

$$100=(2*2*2+2)^2$$

For the rest please help.

number-theory

number-theory

share|improve this question

edited 1 hour ago

jafe

7,5861885

asked 1 hour ago

Pet123

61

New contributor

Pet123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

edited 1 hour ago

jafe

7,5861885

asked 1 hour ago

Pet123

61

New contributor

Pet123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

share|improve this question

edited 1 hour ago

jafe

7,5861885

edited 1 hour ago

jafe

7,5861885

edited 1 hour ago

jafe

7,5861885

7,5861885

asked 1 hour ago

Pet123

61

New contributor

Pet123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 1 hour ago

Pet123

61

asked 1 hour ago

Pet123

61

61

New contributor

Pet123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

New contributor

Pet123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

Pet123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  In case anyone missed it, the same problem with exactly 6 /i/s is trivial: (iii - ii) / i works for any i in any base > i.
  – Rupert Morrish
  32 mins ago
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  In case anyone missed it, the same problem with exactly 6 /i/s is trivial: (iii - ii) / i works for any i in any base > i.
  – Rupert Morrish
  32 mins ago
  

  
  
  
  

In case anyone missed it, the same problem with exactly 6 /i/s is trivial: (iii - ii) / i works for any i in any base > i.
– Rupert Morrish
32 mins ago

In case anyone missed it, the same problem with exactly 6 /i/s is trivial: (iii - ii) / i works for any i in any base > i.
– Rupert Morrish
32 mins ago

add a comment | 

4 Answers
4

active

oldest

votes

up vote
2
down vote

For 9:

$100 = 99 + (frac99)^9$

For 8:

$100 = 88 + 8 + sqrt8+8$

share|improve this answer

answered 1 hour ago

jafe

7,5861885

add a comment | 

up vote
1
down vote

Four

$100 = (frac44 - 44) ^sqrt4$

share|improve this answer

answered 58 mins ago

Rupert Morrish

2,5471725

add a comment | 

up vote
1
down vote

Partial (will update as I figure more out)

For 3:

33*3+(3/3)

For 5:

(5*5*5)-(5*5)

For 7: (possibly cheating?)

ceiling(sqrt(7!)) + ceiling(sqrt(7!)) - (7*7) + 7. you did say any function was allowed.

share|improve this answer

edited 35 mins ago

answered 1 hour ago

Excited Raichu

86315

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  5 could also be (5+5+5+5)*5
  – PotatoLatte
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Definitely cheating to use ceiling and floor, I would think.
  – Rupert Morrish
  34 mins ago
  

  
  
  
  

add a comment | 

up vote
0
down vote

Seven (almost)

$100 = (7 + 7) * (7 + frac7^07)$

share|improve this answer

edited 17 mins ago

answered 25 mins ago

Rupert Morrish

2,5471725

add a comment | 

Your Answer

StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "559"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
convertImagesToLinks: false,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);

Pet123 is a new contributor. Be nice, and check out our Code of Conduct.

 

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f73628%2f100-using-only-5-number-of-digits%23new-answer', 'question_page');

);

Post as a guest

Name Email

4 Answers
4

active

oldest

votes

4 Answers
4

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
2
down vote

For 9:

$100 = 99 + (frac99)^9$

For 8:

$100 = 88 + 8 + sqrt8+8$

share|improve this answer

answered 1 hour ago

jafe

7,5861885

add a comment | 

up vote
2
down vote

For 9:

$100 = 99 + (frac99)^9$

For 8:

$100 = 88 + 8 + sqrt8+8$

share|improve this answer

answered 1 hour ago

jafe

7,5861885

add a comment | 

up vote
2
down vote

up vote
2
down vote

For 9:

$100 = 99 + (frac99)^9$

For 8:

$100 = 88 + 8 + sqrt8+8$

share|improve this answer

answered 1 hour ago

jafe

7,5861885

For 9:

$100 = 99 + (frac99)^9$

For 8:

$100 = 88 + 8 + sqrt8+8$

share|improve this answer

answered 1 hour ago

jafe

7,5861885

share|improve this answer

share|improve this answer

answered 1 hour ago

jafe

7,5861885

answered 1 hour ago

jafe

7,5861885

answered 1 hour ago

jafe

7,5861885

7,5861885

add a comment | 

add a comment | 

up vote
1
down vote

Four

$100 = (frac44 - 44) ^sqrt4$

share|improve this answer

answered 58 mins ago

Rupert Morrish

2,5471725

add a comment | 

up vote
1
down vote

Four

$100 = (frac44 - 44) ^sqrt4$

share|improve this answer

answered 58 mins ago

Rupert Morrish

2,5471725

add a comment | 

up vote
1
down vote

up vote
1
down vote

Four

$100 = (frac44 - 44) ^sqrt4$

share|improve this answer

answered 58 mins ago

Rupert Morrish

2,5471725

Four

$100 = (frac44 - 44) ^sqrt4$

share|improve this answer

answered 58 mins ago

Rupert Morrish

2,5471725

share|improve this answer

share|improve this answer

answered 58 mins ago

Rupert Morrish

2,5471725

answered 58 mins ago

Rupert Morrish

2,5471725

answered 58 mins ago

Rupert Morrish

2,5471725

2,5471725

add a comment | 

add a comment | 

up vote
1
down vote

Partial (will update as I figure more out)

For 3:

33*3+(3/3)

For 5:

(5*5*5)-(5*5)

For 7: (possibly cheating?)

ceiling(sqrt(7!)) + ceiling(sqrt(7!)) - (7*7) + 7. you did say any function was allowed.

share|improve this answer

edited 35 mins ago

answered 1 hour ago

Excited Raichu

86315

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  5 could also be (5+5+5+5)*5
  – PotatoLatte
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Definitely cheating to use ceiling and floor, I would think.
  – Rupert Morrish
  34 mins ago
  

  
  
  
  

add a comment | 

up vote
1
down vote

Partial (will update as I figure more out)

For 3:

33*3+(3/3)

For 5:

(5*5*5)-(5*5)

For 7: (possibly cheating?)

ceiling(sqrt(7!)) + ceiling(sqrt(7!)) - (7*7) + 7. you did say any function was allowed.

share|improve this answer

edited 35 mins ago

answered 1 hour ago

Excited Raichu

86315

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  5 could also be (5+5+5+5)*5
  – PotatoLatte
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Definitely cheating to use ceiling and floor, I would think.
  – Rupert Morrish
  34 mins ago
  

  
  
  
  

add a comment | 

up vote
1
down vote

up vote
1
down vote

Partial (will update as I figure more out)

For 3:

33*3+(3/3)

For 5:

(5*5*5)-(5*5)

For 7: (possibly cheating?)

ceiling(sqrt(7!)) + ceiling(sqrt(7!)) - (7*7) + 7. you did say any function was allowed.

share|improve this answer

edited 35 mins ago

answered 1 hour ago

Excited Raichu

86315

Partial (will update as I figure more out)

For 3:

33*3+(3/3)

For 5:

(5*5*5)-(5*5)

For 7: (possibly cheating?)

ceiling(sqrt(7!)) + ceiling(sqrt(7!)) - (7*7) + 7. you did say any function was allowed.

share|improve this answer

edited 35 mins ago

answered 1 hour ago

Excited Raichu

86315

share|improve this answer

share|improve this answer

edited 35 mins ago

edited 35 mins ago

edited 35 mins ago

answered 1 hour ago

Excited Raichu

86315

answered 1 hour ago

Excited Raichu

86315

answered 1 hour ago

Excited Raichu

86315

86315

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  5 could also be (5+5+5+5)*5
  – PotatoLatte
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Definitely cheating to use ceiling and floor, I would think.
  – Rupert Morrish
  34 mins ago
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  5 could also be (5+5+5+5)*5
  – PotatoLatte
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Definitely cheating to use ceiling and floor, I would think.
  – Rupert Morrish
  34 mins ago
  

  
  
  
  

1

1

5 could also be (5+5+5+5)*5
– PotatoLatte
1 hour ago

5 could also be (5+5+5+5)*5
– PotatoLatte
1 hour ago

Definitely cheating to use ceiling and floor, I would think.
– Rupert Morrish
34 mins ago

Definitely cheating to use ceiling and floor, I would think.
– Rupert Morrish
34 mins ago

add a comment | 

up vote
0
down vote

Seven (almost)

$100 = (7 + 7) * (7 + frac7^07)$

share|improve this answer

edited 17 mins ago

answered 25 mins ago

Rupert Morrish

2,5471725

add a comment | 

up vote
0
down vote

Seven (almost)

$100 = (7 + 7) * (7 + frac7^07)$

share|improve this answer

edited 17 mins ago

answered 25 mins ago

Rupert Morrish

2,5471725

add a comment | 

up vote
0
down vote

up vote
0
down vote

Seven (almost)

$100 = (7 + 7) * (7 + frac7^07)$

share|improve this answer

edited 17 mins ago

answered 25 mins ago

Rupert Morrish

2,5471725

Seven (almost)

$100 = (7 + 7) * (7 + frac7^07)$

share|improve this answer

edited 17 mins ago

answered 25 mins ago

Rupert Morrish

2,5471725

share|improve this answer

share|improve this answer

edited 17 mins ago

edited 17 mins ago

edited 17 mins ago

answered 25 mins ago

Rupert Morrish

2,5471725

answered 25 mins ago

Rupert Morrish

2,5471725

answered 25 mins ago

Rupert Morrish

2,5471725

2,5471725

add a comment | 

add a comment | 

Pet123 is a new contributor. Be nice, and check out our Code of Conduct.

 

draft saved

draft discarded

Pet123 is a new contributor. Be nice, and check out our Code of Conduct.

Pet123 is a new contributor. Be nice, and check out our Code of Conduct.

Pet123 is a new contributor. Be nice, and check out our Code of Conduct.

 

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f73628%2f100-using-only-5-number-of-digits%23new-answer', 'question_page');

);

Post as a guest

Name Email

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

Name Email

Name

Email

Name Email

Name

Email