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When the King of Vortzegia found that there was a petrol shortage, he introduced a petrol rationing system according to the 3-digit number on a car's number plate
People could only buy petrol on:
Monday: If the three digit number was odd
Tuesday: If the Digit sum of the number was greater than ten
Wednesday: If the number was a multiple of 3
Thursday: If the digit sum of the number was less than 15
Friday: if at least 2 of the 3 digits were the same
Saturday: if the three digit number was less than 500
Sunday: if each of the digits was less than six
(A) On which days could a car with the number 726 be filled up with petrol?
(B) The king's limo had a number plate that could be filled up everyday. What was the number on it?
3 Answers | Add Yours
A) The car number is 726
It is even - can't fill up on Monday
The Digit sum = 7+2+6 = 15
It is greater than 10, - can fill up on Tuesday
726/3 = 242
It is a multiple of 3. - can fill up on Wednesday
Digit sum is not less than 15
can't fill up on Thursday
No two digits are same - so can't fill up on Friday
It is not less than 500 - So can't fill up on Saturday
Two digits are not less than 6- So can't fill up on Saturday
So the days the car can fill up on are Tuesday and Wednesday only.
B) King's car.
The king's number should satisfy all the requirments.
If the three digit number is less than 500, the maximum digit it can get for the hundreds place is 4. (either 4,3,2,1)
If each of the digit is less than 6, then tens place and ones place can have any of the following (5,4,3,2,1,0)
The number must be odd, therefore the ones place can only have 5 or 3 or 1.
Therefore all the combinations possible are,
4 5 5
3 4 3
2 3 1
Also it should be a multiple of 3 which means their sum of digits must be also divisible by 3. But we know their sum of digits mut be either 11,12,13 or 14. Therefore the sum of digits must be 12.
There is also another rule which says at least two digits must be equal. That means if two are equal the other must be an even number since the sum is 12, which is even
All the possible combinations for these requirements are,
That means the hundreds place and the tens place can't carry same number, which would result in an even number.
Therefore it should be either hundreds place and ones place or tens place or ones place
The possible numbers for ones place are 1, 3, 5
But the equal digits cannot be 1 or 3, since the sum should be 12. If the two digits is 3, the remaining digit would be 6. Therefore, the equal digit is 5.
The number of the king's car is 255.
i agree with the answer but im not sure if i can ask an extension question here but, here it is: the king wanted the queen to fill up her car on 6 days. What number should appear on the numberplate. Provide all possible answers.
This is a maths challenge problem in Victoria Australia.
The rules of the Challenge forbid online resources and all answers must be your own work.
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