An Antilog Lizard
I was pondering over what problem to give you guys to solve when it suddenly struck me - I could borrow something from at least a hundred years ago, right? So I got hold of this book called (sorry, not telling you because you'll Google it) written by (nope, not opening my mouth for the same reason) with a problem number (deleted) and the answer on page (blank). What I can tell you is that it is copyright 1882. So, let's see if a 19th century problem can be solved easily by 21st century geniuses like you.
While a log, two feet in circumference and 10 feet long, rolls 200 feet down a mountainside, a lizard on top of the log goes from one end to the other, always remaining on top. How far does the lizard move?
(The problem was: "If I were to tell you that I'd bet you a buck if you gave me two bucks I'd give you three bucks in return, would it be a good bet for you to accept?" - MS)
Here, you may choose to argue that you are returning three bucks and so you are winning the bet. Or in order to avoid such a situation, you may not exercise this option at all. In the fourth case, you win the bet and so, I give you a buck. That leaves me with my two bucks. No loss, no gain. Hence, it's obvious that this bet is not good for me to accept because I have no chance of winning unless you decide to lose, with 25 per cent chance of losing and 50 per cent chance of no gain, no loss.
- Balagopalan Nair k, email@example.com
(The second puzzle was: "What remainder would you get when you divide 100^100 by 11?" - MS)
The divisibility rule of 11 is that the difference between the sum of odd digits and sum of even digits is 0 or a multiple of 11. 100^100 = 10^200 = 1 followed by 200 zeros. The number one less than this is 200 consecutive 9s, which is a multiple of 11 in accordance with the rule. Alternatively, 200 consecutive 9s are 100 pairs of 99, hence a multiple of 11. Therefore, the remainder is 1.
- Hasrat Parkar, firstname.lastname@example.org
Numbers like 10, 100, 1000, etc, when divided by 11, leave remainders that follow a strange pattern. If zeros are odd in number, the remainder is 10 and if even, the remainder is 1. As all the powers of 100 have even numbers of zeros, they have a remainder of 1. Hence 100^100 divided by 11 leaves a remainder of one.
- Sheikh Sintha Mathar, email@example.com
(Yes, Minu Moosa, firstname.lastname@example.org; you got it right too. - MS)
(The third one was: can one weigh a powerful magnet on an iron plated kitchen scale which is ferromagnetic?" - MS)
When the magnet wasn't in contact with the scale, the reading that was shown was actually a force exerted by the magnet on the scale, to a person who is seeing the magnet and scale as one system. This force will appear as an internal force. When the system comes in contact, a new force develops: the contact force between the magnet and scale which is opposite to the magnetic force, hence, balancing the magnetic force. In
the end, we are left with gravity as the net force which accounts for the reading on the scale.
- Akshit Chaturvedi, email@example.com
1. A PEAR, an APPLE, a LEMON and a BANANA all add up to an ORANGE. If each letter represents a number between 0 and 9 (both inclusive), solve the equation.
(Submitted by Saifuddin S F Khomosi, firstname.lastname@example.org)
2. What's the only vegetable or fruit that's never sold frozen, canned, bottled, processed, smoked, sundried, salted, stuffed, pickled, cooked or in any other form but fresh? (And let's not have stuff like goji berries, sea kelp, chia seeds or mangosteens. Keep it simple.)
Mukul can be reached at email@example.com