Personal Blogs

The author, Michael Quinion, is a man after my own heart. (I mean because he is an etymologist, he's not looking for a transplant or anything.) His book is really fascinating and a very enjoyable read. I've only read part way through at the minute but when I've finished I'll post a short review. Watch this space!

I'd not heard of this book before and I simply stumbled across when searching for the origin of the phrase 'All at sixes and sevens'.

The phrase is found in Chaucer and Shakespeare with the same meaning as today (to be flummoxed, or in a state of confusion) and from Quinion's book I learned the most probable explanation is that it comes from a dice game where 'sixes and sevens' were proverbially risky bets.

The reason I was looking up the expression is that in my Quora Digest feed the redoubtable Alon Amit answered the question: to prove that for any we can find a -digit number which is divisible by (or some greater power) and entirely made up of the digits and . 

For example today is the 22nd and here is number satisfying those conditions

There are other pairs of digits that could be used instead of and but I think the Original Poster probably recalled the phrase 'at sixes and sevens' and thought those numbers would be a good choice. 

If you are interested here is a Python program that implements Amit's algorithm at the end of this post.

# Generates a number with num digits, all 6s or 7, 
# which is divisble by 2^num or some higher power of 2.

def next(n):
    digits = len(str(n))
    if n % 2**(digits + 1):
        return int('7' + str(n))
    else:
        return int('6' + str(n))

num = 22

n = 6
for step in range(1,num):
    n = next(n)
print(n)