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
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calendarEducator since 2012
write251 answers
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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
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calendarEducator since 2010
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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.