ENIGMATHIC
As you reach Iraq, you come across a poster mentioning a contest which could help you earn more money for your trip. So you decide to participate and below are the questions of the contest.
Question 12:
If you want to build a pile of 100 coins (1 and 2 dinars) such that, number of coins between any two ‘2’ dinar coins is not equal to five, then what are the maximum number of 2 dinar coins that can be included in the pile?
Question 13:
Minimum length of ruler required with 4 marks such that every two marks are at a diff erent distance is 6 as shown in the diagram.
Similarly, what is the minimum length of ruler required with 6 marks such that every two marks are at a diff erent distance?
Question 14:
The government of Iraq wants to issue ‘d’ denominations of coins (in whole numbers of dinars(Iraqi currency)) so that by using no more than 3 coins, citizens can pay any amount from 1 dinar to 36 dinar. Find the value of ‘d’ and all the ‘d’ denominations and give the sum of all these ‘d’ denominations?
(Ex: if d=3 and 3 denominations are {4,5,3}, answer= 4+5+3= 12.)
The answer to question 14 should be 22.
ReplyDeleteThe denominations are 2,5,15.(the method is only possible if the buyer and seller perform some exchange eg.to pay 10 rupees, one can pay 50 rupees and get back 40 rupees.)
Using only these three denominations, and only using three or less coins, one can pay any amount between 1-36dinars.
Eg. To pay 1 dinar,one can pay a 5 dinar coin and get back to 2 dinar coins in return.
To pay 36 dinar coins, one can pay three 15 dinar coins and get back one 5 dinar and two 2 dinar coins(total of 3 coins) in return.
In this manner any amount between 1-36dinars can be paid.
So the answer is sum of denominations=2+5+15=22
Firstly, I would like to make it clear that the question no where meant a two-sided transaction. A person himself should be able to pay any amount between 1 to 36 dinars.
DeleteThough the interpretation was different, we appreciate you for explaining us your solution.
answer to 12 is 99
ReplyDeleteIt is 52
DeleteYes, the answer is 52. If you think that the answer is 99 please give us your solution.
DeletePlz reply to other solutions also.
DeleteIn question 12, there can be 99 two dinar coins and only 1 one dinar coin (99 two dinar coins at the bottom and 1 one dinar coin on the top. There cannot be 100 2 dinar coins since we have to use both the coins)
DeleteBetween any two '2' dinar coins there can't be 5 coins
DeleteThe question !14 is not clear , ONe possible solution is taking numbers 1-35,or 1-34 or 1-36 . andd soo oon , it should have been mentioned if any thing is to be minimised
ReplyDeletethe question 14 can have many solutions .nothing has been mentioned about minimizing the sum . plz reconsider
ReplyDeleteThis comment has been removed by the author.
Deletethe question 14 can have many solutions .nothing has been mentioned about minimizing the sum . plz reconsider
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteIt should be 53 b/c using 1,4,7,8,10,11,12
ReplyDeleteWe can make all possible values ranging from 1-36
WHITOUT TWO WAY TRANSACTION.
Eg. 1→1
1+1→2
1+1+1→3
4→4
4+1→5
4+1+1→6
7→7
8→8
8+1→9
10→10
11→11
12→12
NOW WE CAN REPEAT SEQUENCE
TECHNOTHLON PLZ REPLY
ReplyDeletecan anybody explain me the answer to question 13 as choosing 6 points gives us 15 distances so how can we create a ruler of 17 cm in length
ReplyDeleteEvery two marks should have distinct distances between them. Therefore, as you have calculated 6C2 = 15 will be the minimum length that is required but we cannot be sure that the required condition will be satisfied. Even with length 16 it is not possible. The answer is 17. And one of the possible way of placing all the 6 marks would be 0,3,5,9,16,17.
DeleteIn question 12, there can be 99 two dinar coins and only 1 one dinar coin (99 two dinar coins at the bottom and 1 one dinar coin on the top. There cannot be 100 2 dinar coins since we have to use both the coins)
ReplyDeleteNo. Of coins should not be equal to 5 between any '2' dinar coins
DeleteQues14. 1,2,7,10,11,12 are the required denominations... Plz reconsider
ReplyDelete1,4,6,14,15 is the most optimized solution and thus sum of these numbers 1+4+6+14+15 = 40 is the answer.
DeletePlz reply techniches!!!
ReplyDeleteWe will surely consider your request regarding the 14th question. The question will be rechecked but the most optimized solution is the following where you had to minimize the 'd' value.
Deleted=5, 1+4+6+14+15
But In question u had nowhere said to minimise d
DeleteSo plz check out my solution too
The denominations can be 1 2 4 8 16 respectively which sums to 31
ReplyDeleteYou can't pay 15 with these denominations
DeleteIt should be 53 b/c using 1,4,7,8,10,11,12
ReplyDeleteWe can make all possible values ranging from 1-36
WHITOUT TWO WAY TRANSACTION.
Eg. 1→1
1+1→2
1+1+1→3
4→4
4+1→5
4+1+1→6
7→7
8→8
8+1→9
10→10
11→11
12→12
NOW WE CAN REPEAT SEQUENCE
It should be 53 b/c using 1,4,7,8,10,11,12
ReplyDeleteWe can make all possible values ranging from 1-36
WHITOUT TWO WAY TRANSACTION.
Eg. 1→1
1+1→2
1+1+1→3
4→4
4+1→5
4+1+1→6
7→7
8→8
8+1→9
10→10
11→11
12→12
NOW WE CAN REPEAT SEQUENCE
It should be 53 b/c using 1,4,7,8,10,11,12
ReplyDeleteWe can make all possible values ranging from 1-36
WHITOUT TWO WAY TRANSACTION.
Eg. 1→1
1+1→2
1+1+1→3
4→4
4+1→5
4+1+1→6
7→7
8→8
8+1→9
10→10
11→11
12→12
NOW WE CAN REPEAT SEQUENCE
The and of question 12 should be 46
ReplyDeleteIn each set the arrangements should be 2,2,2,2,2,2,1 sum =13 2 dinars =6
In 7 sets sum =91 2 dinars =6*7=42
The last set is 2,2,2,2,1 sum =9
Total sum = 91+9=100 , total 2 dinars = 42+4=46
And =46
Techniches plz tell what action is taken for Q-14 because it wasn't specified clearly if we had to use minimum value
ReplyDeleteHey plz reconsider it nd reply fast!!!
ReplyDeleteanswer to questions
ReplyDelete12,13,14 respectively are....
52,17,40
thanx....(if anybody need explanation then pls tell)
please anyone tell the answer of 12th question.
ReplyDelete