Neelesh is fond of playing number games. Once when his friends were present
he challenged them. He said that he has thought of a five-digit number and
anyone who guesses it correctly can use his cycle for a full day. ‘To help you,’
he said, ‘I shall provide some clues.’ These were the clues he gave them
(a) It has 3 prime digits.
(b) The 4th digit is the highest among the five digits.
(c) The 2nd is the lowest among the five digits.
(d) Sum of the 2nd and 3rd digits is higher than the sum f the 1st and 5th digits.
(e) The 4th digit is twice the 5th digit.
(f) The 3rd and 4th digits are consecutive digits.
(g) The 1st digit is one smaller than the 3rd digit.
(h) The 5th digit is between the 2nd digit and the 1st digit.
(i) There are no duplicates and the digit 0 doesn’t appar.
(j) Don’t forget that 1 is not a prime.
Can you figure out the five-digit number Neelesh had in mind?
42563 is the closest
u idiot its not possible check ur question noob
To figure out the five-digit number Neelesh had in mind, let's analyze each clue one by one:
(a) It has 3 prime digits:
Prime digits are digits that are only divisible by 1 and themselves. The prime digits are 2, 3, 5, and 7. So our number must have exactly 3 of these digits.
(b) The 4th digit is the highest among the five digits:
Since the 4th digit is the highest, it must be either 7 or 5 because those are the highest prime digits.
(c) The 2nd is the lowest among the five digits:
Similarly, since the 2nd digit is the lowest, it must be either 2 or 3 because those are the lowest prime digits.
(d) Sum of the 2nd and 3rd digits is higher than the sum of the 1st and the 5th digits:
Let's list down the possible combinations of the 2nd and 3rd digits and check the sum for each combination:
- 2nd digit = 2, 3rd digit = 3 (sum = 2 + 3 = 5)
- 2nd digit = 2, 3rd digit = 5 (sum = 2 + 5 = 7)
- 2nd digit = 3, 3rd digit = 2 (sum = 3 + 2 = 5)
- 2nd digit = 3, 3rd digit = 5 (sum = 3 + 5 = 8)
Based on the clue, the sum of the 2nd and 3rd digits is higher than the sum of the 1st and 5th digits. So the only valid combination is when the 2nd digit is 3 and the 3rd digit is 5.
(e) The 4th digit is twice the 5th digit:
Since the 4th digit is the highest and it's either 5 or 7, and also the 5th digit cannot be 0, the only valid option is when the 4th digit is 5 and the 5th digit is 2 (because 2 * 2 = 4, and the 4th digit cannot be 4).
(f) The 3rd and 4th digits are consecutive digits:
The only valid option is when the 3rd digit is 3 and the 4th digit is 5.
(g) The 1st digit is one smaller than the 3rd digit:
Since the 3rd digit is 3, the only valid option is when the 1st digit is 2.
(h) The 5th digit is between the 2nd digit and the 1st digit:
Since the 1st digit is 2, and the only remaining prime digit available is 7, the only valid option is when the 5th digit is 7.
(i) There are no duplicates, and the digit 0 doesn't appear:
We have used each prime digit once and there are no duplicates. And since 0 is not a prime digit, it cannot appear in the number.
(j) Don't forget that 1 is not a prime:
This clue reminds us that 1 is not considered a prime digit.
Based on all the clues, the five-digit number Neelesh had in mind is 23547.