+0

# How to make digits 1-100 with 2,0,2,1

0
2309
14
+36

The instructions for this assignment are:

Use the digits in the year 2021 and the operations +, -, x, ÷, √ (square root), ^ (raise to a power), “!” (factorial), combinations and permutations — along with parentheses, brackets, or other grouping symbols — to write expressions for the counting numbers 1 through 100.

• All four digits must be used in each expression.

• Only the digits 2, 0, 2, 1 may be used.

• The decimal point may be used, as in .2, .02, etc. (repeating decimals as well)

• Multi-digit numbers such as 20 or 201 may be used.

• Double (!!), triple (!!!) or larger factorials are not permitted

Thanks!

(Of course it would be great if someone could give all the digits, but it's fine if you have an idea for some digits.)

Dec 17, 2020
edited by Karinger  Dec 17, 2020

#1
+117575
+4

Well I can do a few to get you started

1 =  2 + 0 - 2 + 1

2  = (2 + 0) / 2  + 1

3  =  2^2 - 1 - 0

4  =  2^2  - 0/1

5 =  2 + 0 + 2 + 1

6 =  (2 + 1)*2  + 0

7  =  10/2 + 2

8  =  (2 + 1)! + 2   - 0

9 =  (2 + 1)^2  + 0/2

10  = (20/2)  / 1

11  = 20 / 2 + 1

12  =  12  + 0/2

13  =   12 + (0/2)!       ( 0!   = 1)

14  =  12 + 2 + 0

15  =  C(10,2) / ( 2! + 0! )

16  =   2^ ( 0! + 1!  + 2!)

17 = 20 - 2 -1

18  =  20  - (2/1)!

19  = 20 - 2! + 1!

20 =   20 / (2 -1)

21  =  20 + 2  - 1

22  =  20 + 2/1

23  = 20 + 2 + 1      (the easiest!!!  LOL!!!)

24  = ( 12) ( 2 + 0)

25 =   12*2  + 0!

26  =  20 + (1 + 2)!

See if  you can do some more.....maybe we can figure  out some  others, too  !!!!\

Dec 17, 2020
#2
+36
+3

Thank you so much! Yeah, I would love to try and find other numbers! I really don't know how you do it.. :)

Karinger  Dec 17, 2020
edited by Karinger  Dec 17, 2020
#3
+117575
+3

Well...to be  honest....I don;t either  !!!

CPhill  Dec 17, 2020
#4
+117575
+3

Some more

39 =   20*2 - 1

40  =10 (2 + 2)

41  = 20 * 2 + 1

60 =  20 ( 2 + 1)

65=  C(12,2) - 0!

66 =  C(12,2) - 0

67   =C(12,2)  + 0!

43 = C (10,2)  - 2

47 = C(10,2) + 2

100  = 102  - 2

98  = 10^2  - 2

Dec 17, 2020
#6
+36
+2

I don't know what to say...you are literally doing it so quick it seems impossible!!

Karinger  Dec 17, 2020
#5
+117575
+3

And

42  = 21*2  - 0

43 =  21 *2  + 0!

63  = 2^( [ 2 + 1]!)  - 0!

64  =  2^([2 + 1)! ] + 0

32 = 10  + 22

50  = 10^2/2

34  = (2^2)! + 10

35  = [ (2 + 1) 1] ^2  - 0!

36  = [ (2 + 1)!  ] ^2  - 0

27  = [ (2 ! + 0! ) ^( 2 + 1)

60  = (10/2)! / 2

Dec 17, 2020
edited by CPhill  Dec 17, 2020
edited by CPhill  Dec 17, 2020
#7
+117575
+2

Maybe I'll think of some more...some will be  difficult  !!!

CPhill  Dec 17, 2020
#8
+36
+2

Don't worry about it - you have done enough!! Only do it if you would like LOL :)

Karinger  Dec 17, 2020
#9
+117575
+2

37  =   (2! + 0!)! ^( 2)  +  1

31  = (2!  + 0!)!  / .2   + 1

99 =  20/.2 - 1

59 =  12/.2  - 0!

61  = 12/.2  + 0!

33  =  2^(1/.2) + 0!

31  =  2^(1/.2) - 0!

52  =  (10/.2) + 2

48 =  (10/.2)  -  2

28  = C(10-2, 2)

90 = C(10,2) * 2

55  = (12 - 0!)/.2

Dec 17, 2020
#10
+36
0

What does C mean, like C(10,2) * 2 and C(10-2, 2)?

Karinger  Dec 17, 2020
#12
+117575
0

C ( a, b)   is  a combination

It counts sets  of things

Let's suppose that we have 10 different  objects  and I want to choose any two  of them....the number of different sets  =   C (10,2)    =  45  different sets

CPhill  Dec 17, 2020
#14
+36
0

Thanks!

Karinger  Dec 17, 2020
#11
+2155
0

Very cool, CPhill!

For an encore, can you do it using... Roman numerals?  MCDXLI LOL ILXDCM

--. .-

GA

Dec 17, 2020
#13
+117575
+1

72   = (12)  ( 2 + 0!) !

Question....we have to use all four digits in each expression......can we repeat any (or all) of these  ???