Digit in the unit place of 3^(3^3) - (3^3)^3 is

M4maths Previous Puzzles

20 Aug 2010 Unit place digit?

Digit in the unit place of
3^(3^3) - (3^3)^3 is

OPtion

1) 6
2) 5
3) 4
4) 7
5) 8
6) 9
7) 0
8) 1
9) 2
10) 3

Solution

3^(3^3) – (3^3)^3
3^27 – 27^3
27^9 – 27^3
(27^3)[(27^6)-1]
(....3)*(....9 -1)
(....3)*(....8)
....4

Correct Option: 3 Best Solution (17)

Bimal   14 years AGO

7-3=4

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Amar   14 years AGO

7-3=4

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A J V   14 years AGO

(3^27)-(27^3)===>7625597484987- 19683====>7-3====>4

Will Meet Next Week....
Vadai Pochu....

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Gunaseelan   14 years AGO

3^27-3^9=last digit is 4

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Dr.Dipin Singh   14 years AGO

3^(3^3) – (3^3)^3 = 3^27- 27^3

Digit in unit place in 3^27 = 7 and digit in unit place of 27^3 is 3.

so Digit in the unit place of
3^(3^3) – (3^3)^3 is7-3=4

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MP    14 years AGO

Digit in the unit place of 3^(3^3)or 3^27 or 3^(4n+3) = 7
Digit in the unit place of 3^9 or 27^3= 3

Digit in the unit place of 3^(3^3) – (3^3)^3 is (7-3)=4

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Dinesh Babu   14 years AGO

the difference between unit digit is 4

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PADMASHREE   14 years AGO

3^(3^3) ends with 7 in the unit place
and (3^3)^3 ends with 3 and the remainder will be 4 in units place, so the option is 3

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Leena   14 years AGO

7-3=4

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Meena   14 years AGO

Digit in the unit place of 3^(3^3) – (3^3)^3 is 7-3=4

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SUDESHNA SEN   14 years AGO

3^1= 3
3^2= 9
3^3= 27
3^4= 81
3^5= 243
3^6= 729
........
so the cycle repeats from 5.
Now, the remainder part of 27/5 is 2, so the last digit of 3^27 will be same as 3^(1+2)= 3^3= 27 or 7.
Now, 27^3= 19683
So, digit in the unit place of 3^(3^3)- (3^3)^3 is 7-3= 4...... Option 3)

Like? Yes (1) | No   

Mamon Sengupta   14 years AGO

3^1= 3
3^2= 9
3^3= 27
3^4= 81
3^5= 243
3^6= 729
........
so the cycle repeats from 5.
Now, the remainder part of 27/5 is 2, so the last digit of 3^27 will be same as 3^(1+2)= 3^3= 27 or 7.
Now, 27^3= 19683
So, digit in the unit place of 3^(3^3)- (3^3)^3 is 7-3= 4...... Option 3)

Like? Yes (1) | No   

Trishita Dasgupta   14 years AGO

3^1= 3
3^2= 9
3^3= 27
3^4= 81
3^5= 243
3^6= 729
........
so the cycle repeats from 5.
Now, the remainder part of 27/5 is 2, so the last digit of 3^27 will be same as 3^(1+2)= 3^3= 27 or 7.
Now, 27^3= 19683
So, digit in the unit place of 3^(3^3)- (3^3)^3 is 7-3= 4...... Option 3)

Like? Yes (1) | No   

ASHOK ROY   14 years AGO

3^1= 3
3^2= 9
3^3= 27
3^4= 81
3^5= 243
3^6= 729
........
so the cycle repeats from 5.
Now, the remainder part of 27/5 is 2, so the last digit of 3^27 will be same as 3^(1+2)= 3^3= 27 or 7.
Now, 27^3= 19683
So, digit in the unit place of 3^(3^3)- (3^3)^3 is 7-3= 4...... Option 3)

Like? Yes (1) | No   

Sudeshna Sengupta   14 years AGO

3^1= 3
3^2= 9
3^3= 27
3^4= 81
3^5= 243
3^6= 729
........
so the cycle repeats from 5.
Now, the remainder part of 27/5 is 2, so the last digit of 3^27 will be same as 3^(1+2)= 3^3= 27 or 7.
Now, 27^3= 19683
So, digit in the unit place of 3^(3^3)- (3^3)^3 is 7-3= 4...... Option 3)

Like? Yes (1) | No   

Parbati Sen   14 years AGO

3^1= 3
3^2= 9
3^3= 27
3^4= 81
3^5= 243
3^6= 729
........
so the cycle repeats from 5.
Now, the remainder part of 27/5 is 2, so the last digit of 3^27 will be same as 3^(1+2)= 3^3= 27 or 7.
Now, 27^3= 19683
So, digit in the unit place of 3^(3^3)- (3^3)^3 is 7-3= 4...... Option 3)

Like? Yes (1) | No   

Somdatta Mukherjee   14 years AGO

3^1= 3
3^2= 9
3^3= 27
3^4= 81
3^5= 243
3^6= 729
........
so the cycle repeats from 5.
Now, the remainder part of 27/5 is 2, so the last digit of 3^27 will be same as 3^(1+2)= 3^3= 27 or 7.
Now, 27^3= 19683
So, digit in the unit place of 3^(3^3)- (3^3)^3 is 7-3= 4...... Option 3)

Like? Yes (1) | No