Question

Recently Mr. And Mrs. Crazy have heard the news about the petrol shortage. The king has introduced to the villagers petrol rationing according to the following system, based on the 3-digit number of each number-plate (000 to 999) of the cars in the village.

People could only buy petrol on certain days as follows:
Sunday: if each of the three digits was less than 6
Monday: if the 3-digit number was odd
Tuesday: if the sum of the three digits was greater than 10
Wednesday: if the 3-digit number was a multiple of 3
Thursday: if the sum of the three digits was less than 15
Friday: if at least two of the three digits were the same
Saturday: if the 3-digit number was less than 500

If Mr. and Mrs. Crazy could refuel their car on any day of the week, what is the number on their car's number-plate?

Answer 1

their car's number-plate is 255

Explanation:

let x,y,z represent the three digits respectively

The given conditions are;

Sunday: if each of the three digits was less than 6

x,y,z < 6

Monday: if the 3-digit number was odd

z = odd numbers less that 6

Tuesday: if the sum of the three digits was greater than 10

x+y+z > 10

Wednesday: if the 3-digit number was a multiple of 3

x+y+z = divisible by 3

Thursday: if the sum of the three digits was less than 15

x+y+z < 15

Friday: if at least two of the three digits were the same

x

Saturday: if the 3-digit number was less than 500

x < 5

(x = 1 to 4)

Since

x+y+z > 10

x+y+z < 15

x+y+z = divisible by 3

Then x+y+z = 12

z is odd numbers less that 6

z = (1,3,5)

x = (1,2,3,4)

y = (1,2,3,4,5)

The only combination that satisfies other conditions is;

x = 2

y = 5

z = 5

their car's number-plate is 255

Answer 2

255

Explanation:

They can buy petrol on all the days, so it must follow these following conditions.

Each of the digits less than 6.

Odd(the last digit can be 1,3, or 5).

Sum of the three digits greater than 10

Multiple of 3. This means that the sum of the digits must be divisible by 3.

Sum of the digits less than 15. So, between 11 and 14.

At least two of the digits are the same

Total value less than 500. Which means that the first digits can be from 1 to 4.

Following all these conditions

The answer is 255