Math Questions and Answers

Start Your Free Trial

I need to produce the numbers 1-31 only using the numerals 1, 2, 3 & 4 in their order. you may use exponents ,+,-,multiplication,division or BEDMASĀ 

Expert Answers info

mlehuzzah eNotes educator | Certified Educator

calendarEducator since 2012

write251 answers

starTop subjects are Math and Literature

I'm not sure how to write all the equations with 1,2,3,4 appearing in order.

But you certainly don't need the factorials:

2^(1+4)-3=29

(1+2)^3+4=31

Here are 19 and 23 in order:

-1+(2+3)*4=19

(1+2)^3-4=23

check Approved by eNotes Editorial

Tushar Chandra eNotes educator | Certified Educator

calendarEducator since 2010

write12,554 answers

starTop subjects are Math, Science, and Business

The numbers 1, 2, 3 and 4 have to be used to arrive at values from 1 to 31 using addition, subtraction, multiplication, division and exponentiation and with appropriate use of brackets.

It is not possible to arrive at all the numbers from 1 to 31 using the 4 numbers 1, 2, 3 and 4 in order. In some cases the order has to be changed.

(1*2) + 3 - 4 = 1

1 + 2 + 3 - 4 = 2

(1*2) + 3 - 4 = 3

1 + 2 - 3 + 4 = 4

1^(2+3) + 4 = 5

1 - 2 + 3 + 4 = 6

(1^2)*3 + 4 = 7

-1 + 2 + 3 + 4 = 8

-1 - 2 + (3*4) = 9

1 + 2 + 3 + 4 = 10

1+(2*3)+4 = 11

1*2^3 + 4 = 12

(1+2)*3+4 = 13

1*2 + 3*4 = 14

1 + 2 + 3*4 = 15

(-1 + 2 +3)*4 = 16

(1+4)*3+2 = 17

(1*2+4)*3 = 18

1+(2+4)*3 = 19

(1*2+3)*4 = 20

(1+2)*(3+4) = 21

2*(3*4-1) = 22

2*3*4-1 = 23

(1+2+3)*4 = 24

1+2*3*4= 25

(1+3*4)*2 = 26

(1+2*4)*3 = 27

(1+2*3)*4 = 28

2*3 - 1 + 4!= 29

(1+4)*2*3= 30

1 + 2*3 + 4! = 31

For 29 and 31, the factorial had to be used. It is not possible to arrive at the result without using that.

check Approved by eNotes Editorial