PYHIYP means:
Put your hands in your pockets i.e. use no calculators, no pen & paper; just your eyes and you brain.
The 1st task, a harbinger to be followed by many others, is to prove just by observation and common sense that none of the four numbers listed below is a prime.
i. 5,234,567,896,743
ii. 1,438,525,775,258,341
iii. 77,112,356,378,491
iv. 1,431,436,216,211,339
No time limit!
No cheating!
KISS!
Post your conclusions.
(In reply to
Puzzle Solution: (i) by K Sengupta)
(ii)
(a) For the initiated
The given number is a palindrome having 16 digits. Since any even number palindrome must be a multiple of 11, it follows that the given number cannot be a prime number.
(b) For the uninitiated
The digits in odd positions are: 1,3,5,5,7,2,8,4
The digits in even positions are: 4,8,2,7,5,5,3,1
Since the respective 8 digits in the odd positions and even positions are permutations of each other, it follows that the respective sums of their digits in the odd positions and, the even positions are equal. Accordingly, the difference between their sums is zero, and consequently the number is divisible by 11.
Therefore, the given number cannot be a prime number.
Puzzle Solution: (ii)
