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 in the number whose sum is 11.

Find the number.

## 9 comments:

Answer = 65292

65292

ditto

65292

Since no one explained how they reached that combination, I think I should.

First of all, I think the last sentence should be modified. In fact, saying "There are 3 pairs in the number whose sum is 11" means

the number has a sum of 11i.e. the sum of its digits is 11. IMHO saying"the number has 3 pairs whose sum is 11"would avoid confusion.Now for the solution.

There are 5 digits, let's call them

a,b,c,d,eThe 4th digit is 4 greater than the second digit,

d = b+4

while the 3rd digit is 3 less than the 2nd digit.

c = b-3

The 1st digit is thrice the last digit.

a = 3*e

This means that there are only 2 variables,

bande, since all the others can be written in terms ofbande.b MUST be greater than or equal to 3, otherwise

cwill be negativeb MUST be less than or equal to 5, otherwise d will be 10 or more (i.e. not a single digit)

e is between 0 and 3. 4 or more would put

ain the double digits.There are 10 possible pairs (Combination of 5-choose-2) of which 5 can never be 11;

a+e = 3e+e = 4e can never be 11 if e is an integer

b+c = 2b - 3 can't be more than 7

b+d = 2b + 4 can't be 11 if b is an integer

b+e can't be more than 8

c+e = b+e-3 can't be more than 5

Furthermore,

a+ d can only be 11 if b=4 and e=1, and this makes it the onlt pair with a sum of 11.

So we eliminate these 6 pairs, and we are left with 4 pairs, 3 of which must sum up to 11.

The most obvious one is c + d because it only depends on b (c + d = b - 3 + b + 4 = 2b + 1)

Solving for b we get b = 5

the pair a + b = b + 3e

solving a + b = 11 gives us e = 2

with b = 5 and e = 2 the pair (d+e) will also sum up to 11 and thus we have our 3 pairs.

a = 3e = 3*2 = 6

b = 5

c = b -3 = 2

d = b +4 = 9

e = 2

well explained.............

so confusing..

very well explained........... mr. whats ur email id .. i wanna add u

65292

Post a Comment