# Safe key decrypt puzzle

There is a safe with a 5 digit number as the key. The 4th digit is 4 greater than the second digit, while the 3rd digit is 3 less than the 2nd digit. The 1st digit is thrice the last digit. There are 3 pairs whose sum is 11.

Find the key to open the safe.

let 5 digits be

a b c d e

now,

eq1=> d= 4+b,

eq2=> c = b- 3

eq3=> a =3e,

As a,b,c,d,e are single digits can varies from 0-9

so

bmax <= 5 , from eq1

bmin >= 3, from eq

similarly

dmax = 9

dmin = 7

cmax = 2

cmin= 0

e can be 0, 1,2,3

a will be 0,3,6,9 respectively

So ranges are

0<=a<=9

3<=b<=5

0<=c<=2

7<=d<=9

0<=e<=3

Possible pairs are

ab, ac, ad, ae, bc, bd, be, cd, ce, de

Also there are only three pairs whose sum should be 11

there are 9 cases lets find one by one

a.) if b= 3 => then c = 0, d= 7

(i) a = 9, e= 3,

or (ii) a = 6, e = 2,

or (iii) a = 3, e =1

b.) if b = 4 => then c=1, d=8

(i) a = 9, e= 3,

or (ii) a = 6, e = 2,

or (iii) a = 3, e =1

c.) if b = 5 => then c=2, d= 9

(i) a = 9, e= 3,

or (ii) a = 6, e = 2,

or (iii) a = 3, e =1

So from this only c(ii) shows the desired result

a+b= 11, c+d =11, d+e = 11

so answer is

a=6,b=5,c=2,d=9,e=2

ie. 65292

### Your Answer

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