1.

Replace the letter by digit so that the following calculation are correct A9 2B 97​

Answer»

Answer:

Let N be the 5 DIGIT number JOINT .

Let J+O+I+N+T=S

REQUIRED : (J+O+I+N+T)3=JOINT=N(1)

minimum value of N is 10234 and maximum value 98765

10234−−−−−√3≤S≤98765−−−−−√3

21

But maximum possible S=9+8+7+6+5=35

21

N=104J+1000O+100I+10N+T

Take MOD w.r.t 9

Since 10n≡1mod9

N≡J+O+I+N+T≡Smod9.

THEREFORE S3≡Smod9

this is possible if mod values are −1,0 or 1

So eligible values of S consistent with (2)are26,27,28 and 35

263=17576; Digits are not distinct.Discard.

273=19683; Digits are distinct ; 1+9+6+8+3=27 . O.K.

283=21952; Digits are not distinct.Discard.

353=42875; Digits are distinct ; 4+2+8+7+5=26≠35. Discard.

So only solution is 19683


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