Spirit of 76 with no products (Posted on 2004-07-13)

	Submitted by e.g.
Rating: 3.3333 (3 votes)
Solution:	(Hide)
I'll show this as an algorithm. Start with N=2^76 (given) Set K=N Set I=1 While I isn't greater that 76 look at the I-th digit of N, from the right while it isn't a 6 or 7, add K to N Multiply K by 10 Add 1 to I Take the 76 leftmost digits of N as the answer. At the end (before taking the 76 leftmost digits), N can be written as Px10^76+Q, and Q is written with sixes and sevens only. Since N and Px10^76 are multiple of 2^76, it follows that Q also is a multiple of 2^76, and that's the why of the last instruction of the algorithm. On average, the "add K to N" order is done twice, so we need about 152 sums to solve the problem.

	Subject	Author	Date
	My solution	Federico Kereki	2004-07-17 21:36:32
	re: No Subject	Federico Kereki	2004-07-16 18:32:00
	No Subject	Cory Taylor	2004-07-16 17:23:59