Question

(J+o+i+n+t)3 = joint find for what value of joint you will get the same numerical value as joint
( plz answer it )​

Answer 1

Given :- (J+o+i+n+t)³ = joint find for what value of joint you will get the same numerical value as joint ?

Solution :-

since JOINT is a 5 digit number so,

→ Minium possible value of J + O + I + N + T = 22 (because 22³ = 10648 )

→ Maximum possible value of J + O + I + N + T = 46 (because 46³ = 97336 )

now, from 22 to 46 checking the sum of cube that is ewual to given number we get,

• 22³ = 10648 => 1 + 0 + 6 + 4 + 8 = 19 ≠ 22 .
• 23³ = 12167 => 1 + 2 + 1 + 6 + 7 = 17 ≠ 23 (or we can say that, all 5 digits are not unique in 12167 , since 1 is repeated .)
• 24³ = 13824 => 1 + 3 + 8 + 2 + 4 = 18 ≠ 24 .
• 25³ = 15625 => 1 + 5 + 6 + 2 + 5 = 19 ≠ 25 .( or 5 is used twice.)
• 26³ = 17567 => 1 + 7 + 5 + 6 + 7 = 26 = 26 .
• 27³ = 19683 => 1 + 9 + 6 + 8 + 3 = 27 = 27 .
• Numbers greater than 27 will not possible .
• Also maximum sum without repeated digits will be 9 + 8 + 7 + 6 + 5 = 35 . { we just have to check upto 35. }

now, we gets two number 26³ and 27³ . As we can see that, in 26³ number 7 is repeated twice and in JOINT no alphabet is repeated . Therefore, this case is not possible .

Hence, we can conclude that,

→ 27 * 27 * 27 = 19683

→ (1 + 9 + 6 + 8 + 3) * (1 + 9 + 6 + 8 + 3) * (1 + 9 + 6 + 8 + 3) = 19683

→ (J + O + I + N + T) * (J + O + I + N + T) * (J + O + I + N + T) = JOINT

→ (J + O + I + N + T)³ = JOINT .

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Answer 2

Given : ( j + o + i + n + t )³  = joint

To Find :  value of joint you will get the same numerical value as joint

Solution:

joint = 19683

(1 + 9 + 6 + 8 + 3)³  =  27³  =  19683

Minimum value of joint  =   10234            

Maximum Value = 98765

Minimum value of  j + o + i + n + t  =   10      

Maximum Value of  j + o + i + n + t  = 35

Hence    ∛10234      ≤  j + o + i + n + t    ≤  ∛ 98765

=>  22  ≤  j + o + i + n + t    ≤  35

Solving further we get :

(1 + 9 + 6 + 8 + 3)³  =  27³  =  19683

22³ = 10648    sum of digit ≠ 22

23³ = 12167     sum of digit ≠ 23

24³ = 13824    sum of digit ≠ 24

25³ = 15625     sum of digit ≠ 25

26³ = 17576    sum of digit = 26 but digits are not distinct

27³ = 19683     sum of digit  = 27    required solution

28³ =21952    sum of digit ≠ 28

29³ =24389     sum of digit ≠ 29

30³ =27000    sum of digit ≠ 30

31³ = 29791     sum of digit ≠ 31

32³ = 32768     sum of digit ≠ 32

33³ = 35937     sum of digit ≠ 33

34³ = 39304   sum of digit ≠ 34

35³ = 42875   sum of digit ≠ 35

Hence only solution is  

27³ = 19683     sum of digit  = 27    required solution

J = 1 , O  = 9  ,  I = 6  , N = 8  , T  = 3

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