In how many ways can a lock be opened if that lock has three digit number lock if i) the last digit is 9ii) and sum of the first two digits is less than or equal to the last digit.numbers are from 0-9

our number is xy9 now if x is 0 then y has 10 options now if x is 1 then y has 9 options (except 9) now if x is 2 then y has 8 options (except 9 and 8) . . . now if x is 9 then y has 1 option (that is 0)

so the answer is 1 + 2 + ... + 10 = 55

Showing Answers 1 - 36 of 36 Answers

suresh

May 30th, 2005

55

Mubeen

Jul 2nd, 2005

Can u please work this out as i am thinking the answer is 65. Since 1st digit = 0-5 2nd digit = 0-5

Mubeen

Jul 2nd, 2005

Can u please work this one out as i am thinking the answer is 65. Since 1st digit = 0-5 2nd digit = 0-5 3rd digit = 9 always So considering all the combinations u still have two 5's that can combine with every other number except each other so u have missed those 10 combinations.

kavita kanyal

Jul 7th, 2005

Ans : 55

Soumya

Jul 25th, 2005

Since the last digit is 9... the sum of the first two digits shud not exceed 9... so the possible combinations are only: 0-9, 1-8, 2-7, 3-6, 4-5, 5-4, 6-3, 7-2, 8-1, 9-0. So, totally 10... Answer: 10

oktay

Aug 23rd, 2005

our number is xy9 now if x is 0 then y has 10 options now if x is 1 then y has 9 options (except 9) now if x is 2 then y has 8 options (except 9 and 8) . . . now if x is 9 then y has 1 option (that is 0)

This is variou combination, for the first two key add together 55

bnreddy

Jan 30th, 2007

the answer is 45.because in the number,first digit fill starts with 1and second digit in between 0-8 only=9 first digit fills start with 2 and second digit in between 0-7 only=8 as it is . .......................3.....................................................0-6..........=7.....................................................................................4....................................................0-5...........=6 5...................................................0-4.............=5 6 0-3.............=4 7 ...........................................0-2............=3 8...................................................0-1.............=2 9...................................................0...............=1total=9+8+7+6+5+4+3+2+1=45 ANSWER.HERE NEVER FORGET THE RULES THAT ARE THREE DIGIT NUMBER SO IT NEVER STARTS WITH ZERO. AND THE NUMBER IS LESS THAN OR EQUAL TO 9.

Ashish taunk

Apr 1st, 2007

ans: 55 see we have the sum of 1st two digits is not more than 9; so for 1st digit is 0,there are 10 combinations of two digit no(i.e. 00,01,02,03,....,09); for 1st digit is 1,there are 9 combinations of two digit no(i.e. 10,11,12,13,....,18); for 1st digit is 2,there are 8 combinations of two digit no(i.e. 20,21,22,,....,27); for 1st digit is 3,there are 7 combinations of two digit no(i.e. 30,31,32,33,....,36); . . . . for 1st digit is 7,there are 3 combinations of two digit no(i.e. 70,71,72); for 1st digit is 8,there are 2 combinations of two digit no(i.e. 80,81); for 1st digit is 9,there is only 1 combination of two digit no(i.e. 90);

so totoal no of combinations we have = 10+9+8+.....+3+2+1 = 10 (10 + 1) / 2 = 55

gurjot

Apr 4th, 2007

look ppl the question says that the sum of first two digits should not exceed 9.. therefore if the first digit is: 0 the possible combinations will be 0,1,2,3,4,5,6,7,8,9....therefore the number of combinations is 10 1 the possible combinations are 0,1,2,3,4,5,6,7,8.. therefore 9 2................8 3................7 4................6 5................5 6.................4 7.................3 8.................2 9..................1

that makes a total of 55 combinations.. so there are 55 possible combinations..

Harish A

Apr 18th, 2007

Answer is 55

kishore vemuri

Jun 26th, 2007

see there if 1'st is 0 - 10 chances for the second 1 - 9 2 - 8 3 - 7 ................ we will have (10+9+8+7+6+5+4+3+2+1)=55

The lock can be opened in only 1 way, depending upon the code that was used while locking it

pavan kumar karasala

Jul 24th, 2007

55 is the correct answer.............. first two digits sum must be less than or equal......... 0-9 1-8 2-7 . . . . 9-0 these are the digits that are ar equal to 9 =10 digits and what abt which are leass than 9

similarly their total must be equal to 8,7,6,5,4,3,2,1,0......... so for total of 9 we have 10 digits....... for total of 8 we have 9 digits.. 8,7,6,5,4,3,2,1...........so the total is 55.

karan

Jul 24th, 2007

I feel the answer should be 1 .

as every lock can be opend by only one combination that sets it free!

This is my tought please reply if you agree ! i feel the other stats are simply to misguide.

bonthala narsimha reddy

Jul 28th, 2007

Answer is 45. because number is 3 digit number. so in first digit can fill up with only 1 to 9. due to second rule , 2nd digit fill up with only 0 to 8. because 2nd one is less than or equal to 9 only. so like series is 109 119 . . . . 189 . 209 . 289 . 909.

ramprasad

Aug 10th, 2007

55 is the correct answer Since the last digit is 9 there are only 55 ways in which the first two digits can be placed.

uma

Aug 15th, 2007

Let the No. be xy9. x cannot be 0, because the no will become 2 digit no. x can be from 1-9. y can be anything between 0-9. and x+y=9. so the possibilities are

Answer is ii) and sum of the first two digits is less than or equal to the last digit.

numbers are from 0-9

sakshi

Sep 9th, 2017

The digits might repeat.

Azharuddin Khan

Oct 29th, 2017

Answer will be 55.
As last digit is fixed as 9. so there are only 2 digits which we can set according to first possibility.
Now according to second possibility sum of both remaining digits should not be greater than 9, so
If we put 0 at first place then we can place 10 digits from 0 to 9 at second position, so 10 possibilities.
If we put 1 at first place then we can put 9 digits 0-8 at second place, so 9 possibilities at second position.and so on.
so possible ways are 10+9+8+7+6+5+4+3+2+1=55.

## In how many ways can a lock be opened if that lock has three digit number lock if i) the last digit is 9ii) and sum of the first two digits is less than or equal to the last digit.numbers are from 0-9

This question is related to Accenture Interview## Editorial / Best Answer

Answered by: oktay

our number is xy9

now if x is 0 then y has 10 options

now if x is 1 then y has 9 options (except 9)

now if x is 2 then y has 8 options (except 9 and 8)

.

.

.

now if x is 9 then y has 1 option (that is 0)

so the answer is 1 + 2 + ... + 10 = 55

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