1 2 3 4 5 6 7 8 9 = 1

     
This question inspired me to lớn write the same puzzle but instead replace the "= 100" with "= 1" with similar requirements & restrictions.

Bạn đang xem: 1 2 3 4 5 6 7 8 9 = 1

What is the expression with the fewest number of operators inserted that evaluates to lớn 1?

Restrictions:

The numbers need khổng lồ be in the order that"s shown in the question.Only use the operators +,−,×,÷ and √ & ! (Implies that modulus "%", exponent "^", binomial coefficients, & other operators are not allowed).Parentheses will not be counted, so they can be used to lớn change the order of operations.Rounding is not allowed, so it have to lớn equal to 1.

Verify your calculations in that calculator application that comes with your PC, if it ever did came with your PC.

This is my first time writing a puzzle here so obviously I should have thought this out a lot more instead of adding rules when situation comes.


mathematics calculation-puzzle formation-of-numbers
chia sẻ
Improve this question
Follow
edited Apr 13, 2017 at 12:50
*

CommunityBot
1
asked Apr 15, năm ngoái at 20:35
*

John OdomJohn Odom
26711 gold badge33 silver badges1212 bronze badges
$endgroup$
7
| Show 2 more comments

12 Answers 12


Sorted by: Reset to default
Highest score (default) Date modified (newest first) Date created (oldest first)
39
$egingroup$
If √ can mean nth root:

$$sqrt<1234567>-8+9$$

3 operators. Obviously...


tóm tắt
Improve this answer
Follow
answered Apr 16, 2015 at 6:11
*

user23013user23013
1,09899 silver badges1515 bronze badges
$endgroup$
3
địa chỉ a phản hồi |
22
$egingroup$

uses four. (I wrote a Python script.)


cốt truyện
Improve this answer
Follow
answered Apr 15, năm ngoái at 20:52
*

LynnLynn
2,4051010 silver badges2121 bronze badges
$endgroup$
5
showroom a phản hồi |
11
$egingroup$
How many significant digits matter here for rounding? Because if it"s anything less than $3,456,789$ zeroes, I can solve it in three ;)

$1+2/3456789! = ~1$

Many programming languages will evaluate it as "1". Even Wolfram Alpha can"t show me enough decimal digits to tell me I"m wrong ;P

EDIT:Yes, I know this is no longer valid as of the rule change that doesn"t include rounding. I didn"t expect it would be allowed anyways, just figured it would be worth submitting, since it comes so infinitesimally close to 1. Besides, kgull managed to lớn get even closer using a similar method.


mô tả
Improve this answer
Follow
edited May 1, 2018 at 4:25
*

SteamCode
3,15333 gold badges1313 silver badges3131 bronze badges
answered Apr 15, năm ngoái at 21:02
Mwr247Mwr247
52533 silver badges66 bronze badges
$endgroup$
4
địa chỉ cửa hàng a bình luận |
5
$egingroup$
Assuming the binomial coefficient is not an operator itself and parentheses are allowed and not counted, this requires only 1 operator.

$$1+2345choose6789=1$$

Check the Pochhammer symbol too:

$$1+(-2)_3456789$$

Some useful information on Wolfram Alpha.

Xem thêm: Công Thức Tính Delta, Delta Phẩy Phương Trình Bậc 2, Delta Là Gì


tóm tắt
Improve this answer
Follow
edited Jun 25, năm ngoái at 17:35
grg
20733 silver badges66 bronze badges
answered Apr 16, năm ngoái at 13:51
Francesco De LisiFrancesco De Lisi
17522 bronze badges
$endgroup$
8
| Show 3 more comments
4
$egingroup$
If parentheses will not be counted and if we could use it as multiply:

$12(34)-5(67)-8(9) = 1$

I used only 2 operators.


nói qua
Improve this answer
Follow
edited May 1, 2018 at 3:49
JMP
35.4k77 gold badges7575 silver badges145145 bronze badges
answered Apr 16, 2015 at 21:07
AlexAlex
8,5381818 silver badges6161 bronze badges
$endgroup$
3
add a bình luận |
3
$egingroup$
$$(1 + 23 + 45 + 6! - 789)! = 1$$

$$((1+2-3) imes456789)!=1$$

Everyone is trying with minimum operators.I guess, with
user23013"s solution, we can try with various possibilities :)


nội dung
Improve this answer
Follow
edited Jun 17, 2020 at 8:22
CommunityBot
1
answered Apr 17, 2015 at 8:57
thepacethepace
2,88711 gold badge1111 silver badges1111 bronze badges
$endgroup$
1
địa chỉ a comment |
2
$egingroup$
A simple expression that is exact, & only uses four operations without bending the rules (if exponentiation isn"t permitted, I assume that neither is using the numbers to create n-th roots) while using at least one non-basic operation, is$$((1+2-3) imes456789)!$$That"s one addition, one subtraction, one multiplication, và one factorial (actually, zero factorial, but you know what I mean). Another similar option is$$((12/3-4) imes56789)!$$A slightly more bendy solution using the fact that negative integer factorials can be considered to lớn be infinite is$$1+2/(3-456789)!$$


chia sẻ
Improve this answer
Follow
answered Apr 17, năm ngoái at 7:54
Glen OGlen O
4,93311 gold badge1414 silver badges3131 bronze badges
$endgroup$
địa chỉ a phản hồi |
1
$egingroup$
Three Operators

Similar idea to Mwr247"s solution, but even more significant figures:

$$left(frac123456789! ight)! = 1$$

Wolfram Alpha seems to think it is exactly 1. Good enough for me >_>


nói qua
Improve this answer
Follow
edited Jun 25, 2015 at 17:35
grg
20733 silver badges66 bronze badges
answered Apr 16, 2015 at 6:42
Kyle GKyle G
30711 silver badge1010 bronze badges
$endgroup$
6
| Show 1 more bình luận
0
$egingroup$
$$1-23+45+67-89$$uses only 4 operators.


nội dung
Improve this answer
Follow
edited Jun 25, 2015 at 17:36
grg
20733 silver badges66 bronze badges
answered Apr 15, 2015 at 21:08
My Life for AuirMy Life for Auir
7755 bronze badges
$endgroup$
1
địa chỉ a bình luận |
0
$egingroup$
Edit: I realized Alex did it using 2 operations using this loophole so this is nothing special. I"d delete this normally but I think this solution is still kinda cool.

I got three operations without using an nth root:

$(12)(3)(4)(.5)(-6+7)/((8)(9))=1$Taking advantage of parentheses not counting. (Yes I know the rule wasn"t meant for them to lớn be used this way but I spent a long time thinking of how to lớn exploit this loophole so cut me some slack.)


nội dung
Improve this answer
Follow
edited Jun 26, năm ngoái at 3:54
answered Jun 26, 2015 at 3:46
QuarkQuark
6,04711 gold badge1818 silver badges4545 bronze badges
$endgroup$
địa chỉ cửa hàng a phản hồi |
-3
$egingroup$
In languages lượt thích C# & Java dividing two integers will always result in an integer (decimals will be omitted).Therefore only one operation is required to solve this problem:

12345/6789Which will result in 1.


cốt truyện
Improve this answer
Follow
answered Apr 16, năm ngoái at 12:28
Mike.Mike.
2111 bronze badge
$endgroup$
5
địa chỉ a comment |
-4
$egingroup$
One operator.

Taking advantage of user23013 "s loop hole.

Xem thêm: Nhung Câu Noi Buon Ve Tinh Yeu

If √ can mean nth root:

$$sqrt<23456789>1$$


tóm tắt
Improve this answer
Follow
answered Apr 16, 2015 at 10:42
user288447user288447
101
$endgroup$
1
add a comment |
Highly active question. Earn 10 reputation (not counting the association bonus) in order to answer this question. The reputation requirement helps protect this question from spam and non-answer activity.

Not the answer you're looking for? Browse other questions tagged mathematics calculation-puzzle formation-of-numbers or ask your own question.


Featured on Meta
Linked
78
Making π from 1 2 3 4 5 6 7 8 9
47
1 2 3 4 5 6 7 8 9 = 100
12
123456789=1 problem
Related
47
1 2 3 4 5 6 7 8 9 = 100
0
Smallest impossible positive integer with 5 ones & 5 operators
24
Make numbers 1 - 30 using the digits 2, 0, 1, 8
3
Make numbers 1-30 using 2, 0, 1, 9
11
Create the numbers 1 - 30 using the digits 2, 0, 1, 9 in this particular order!
1
Create Numbers 1 - 100 using 1,9,6,8
3
1 0 1 0 1 0 1 0 1 0 1
15
Make 24 using exactly three 3s
7
9 8 7 6 5 4 3 2 1 = 0 & 1 2 3 4 5 6 7 8 9 = 0
Hot Network Questions more hot questions
Question feed
Subscribe khổng lồ RSS
Question feed khổng lồ subscribe lớn this RSS feed, copy và paste this URL into your RSS reader.


goodsmart.com.vn
Company
Stack Exchange Network
Site thiết kế / biệu tượng công ty © 2022 Stack Exchange Inc; user contributions licensed under cc by-sa. Rev2022.6.14.42365


Your privacy

By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device & disclose information in accordance with our Cookie Policy.