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A Simple Arithmetic Teaser !


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10 hours ago, Sensei said:

I have extension to your teaser:

Make 0 using once each 2, 11, 13, 17, 19, 101 with only + - x / ( ) as Operators.

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(17-2)*(19-13)+11-101 = 0

 

Very nice. There are many other numbers possible too !

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14 hours ago, md65536 said:

I got (101+11+19-17)/2-13=44.

Excellent !

Perhaps getting 22 using once each 11, 13, 17, 19, 101 with only + - x / ( ) as Operators might be tougher !

I wanted to have 6 numbers and therefore added 2 !

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10 hours ago, Commander said:

Perhaps getting 22 using once each 11, 13, 17, 19, 101 with only + - x / ( ) as Operators might be tougher !

Not for me.. ;)

(((13×17)-19)×11)/101=22

 

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I was curious about how many answers there might be, so I wrote code. I gave up before trying to deal with parentheses, but got the following:

(11 - 17) * 13 + 2 + 19 + 101 = 44
(11 - 13) * 19 - 17 - 2 + 101 = 44
(13 + 101) / 2 - 11 - 19 + 17 = 44
(11 - 13 - 17) * 2 - 19 + 101 = 44
(13 - 17 - 19) * 2 - 11 + 101 = 44
(17 - 19 - 2) * 11 - 13 + 101 = 44
(17 - 19) * 11 * 2 - 13 + 101 = 44
(13 - 11 + 19 + 101) / 2 - 17 = 44
(11 - 17 + 19 + 101) / 2 - 13 = 44   (my answer)
((17 - 19 + 101) / 11 + 13) * 2 = 44
((13 * 17 - 19) / 101 + 2) * 11 = 44
((19 - 11) * 17 - 13 - 101) * 2 = 44
(13 * 17 - 19) / 101 * 2 * 11 = 44   (Commander's answer, ignoring order)

Sensei's answer isn't here because it's not left-to-right order of operations. I wouldn't doubt this is a small fraction of the possible answers, but neither would I bet that it is. (I also manually culled duplicates so I may have removed too many.)

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Let's try this new one :

Make 4321 using all these numbers only once 2,3,5,7,11,13,17 with operators + - x / and Brackets.

Another one :

In this sentence, the number of occurrences 
Of the digit 0 is__?
Of the digit 1 is__?
Of the digit 2 is __?
Of the digit 3 is __?
Of the digit 4 is__?
Of the digit 5 is__?
Of the digit 6 is __ ?
Of the digit 7 is __?
Of the digit 8 is__?
Of the digit 9 is __?

Please fill in the blanks.

Make the sentence valid !

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2 hours ago, Commander said:

Let's try this new one :

Make 4321 using all these numbers only once 2,3,5,7,11,13,17 with operators + - x / and Brackets.

Another one :

In this sentence, the number of occurrences 
Of the digit 0 is__?
Of the digit 1 is__?
Of the digit 2 is __?
Of the digit 3 is __?
Of the digit 4 is__?
Of the digit 5 is__?
Of the digit 6 is __ ?
Of the digit 7 is __?
Of the digit 8 is__?
Of the digit 9 is __?

Please fill in the blanks.

Make the sentence valid !

 

There are several options.

Replace all the blanks with "one".

Replace all the blanks with ">=1"

Replace all the blanks with "unimportant".

Replace all the blanks with "less than 99"

 

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On 1/27/2021 at 5:39 PM, John Cuthber said:

There are several options.

Replace all the blanks with "one".

Replace all the blanks with ">=1"

Replace all the blanks with "unimportant".

Replace all the blanks with "less than 99"

 

Hi,

Only positive numbers to be used to fill in the blanks. Also no leading zero too such as 02 etc

Edited by Commander
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On 1/27/2021 at 11:03 AM, Commander said:

In this sentence, the number of occurrences 
Of the digit 0 is__?
Of the digit 1 is__?
Of the digit 2 is __?
Of the digit 3 is __?
Of the digit 4 is__?
Of the digit 5 is__?
Of the digit 6 is __ ?
Of the digit 7 is __?
Of the digit 8 is__?
Of the digit 9 is __?

Please fill in the blanks.

Make the sentence valid !

Some irrational numbers e.g. PI have infinite number of digits of each kind in decimal numerical system.

Edited by Sensei
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On 1/24/2021 at 11:52 PM, Sensei said:

Not for me.. ;)

 

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(((13×17)-19)×11)/101=22

Good !

 

 

13 hours ago, Sensei said:

Some irrational numbers e.g. PI have infinite number of digits of each kind in decimal numerical system.

No irrational Numbers. Simple Positive Integers.

There are 2 Solutions known. You need to find both !

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8 hours ago, Commander said:

There are 2 Solutions known. You need to find both !

It's a bit confusing because it's not a valid sentence with all of those question marks, but if they're changed to commas, one solution is

Spoiler

1, 11, 2, 1, 1, 1, 1, 1, 1, 1

Is this the easier solution?

Oh I see, just by trying some things out:

Spoiler

1, 7, 3, 2, 1, 1, 1, 2, 1, 1

 

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12 hours ago, md65536 said:

It's a bit confusing because it's not a valid sentence with all of those question marks, but if they're changed to commas, one solution is

  Reveal hidden contents

1, 11, 2, 1, 1, 1, 1, 1, 1, 1

Is this the easier solution?

Oh I see, just by trying some things out:

  Reveal hidden contents

1, 7, 3, 2, 1, 1, 1, 2, 1, 1

Absolutely Right ! Well done !

Yes, the first solution is easier and the second is harder !

2 + to you ! If I could give.

Yes the Question marks can be removed.

 

 

Edited by Commander
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