Logic Puzzle 4

After I told someone the answer to my second puzzle (which can be found here: https://jiffyrohan.wordpress.com/2013/01/15/logic-puzzle-of-the-week-250/) they became quite angry, and immediately set me this as a counter-puzzle. It’s quite difficult, and not to be taken literally.

Prove that 70/7 = 500

Solution to Puzzle 3

Start with the more factual statements, such as the fact that the most recent coin is also of the highest value. This means that the ten-rupee coin was minted in 2012. Also, since the second-oldest coin is worth two rupees, the 1976 coin has a value of two rupees.

 
The coin in the centre is of the lowest value, so the one-rupee coin has a position of 4 (from the left, which is how I will define position from here onwards). Since there are two pairs of years using the same digits (1967 and 1976; 1989 and 1998) these must have positions 2, 3, 4 and 5, though we do not yet know the order.
 
Since the coin with position 2 was minted in 1989, the fourth coin, worth 1 rupee, was minted in 1998.
 
Because 1991 and 2002 are palindromic, their corresponding coins must be on the far left and far right (not necessarily respectively).
 
As the oldest coin is third from the right, position 5 has a year of 1967, and so position 3 has a year of 1976.
 
So far, all positions apart from 6 have been filled, and all years apart from 2012 have a place. Therefore, the coin minted in 2012, worth 10 rupees, has position 6.
 
The two five-rupee coins are next to each other, and the only two consecutive positions without a value are 1 and 2. Now, the two remaining values are both 2, so these can be filled in.
 
Finally, the coin on the immediate left of position 7 was minted in 2012. Of 1991 and 2002, only 1991 is more than ten years older than the 2012 coin. Fill in 2002 on the extreme left, and 1991 on the extreme right, and you’re done! The final solution is:Image

Solution to Puzzle 2

The answer is 8.

I know, that’s not what most of you were expecting. I did get some answers that were on the right track, but were not quite correct. At first glance, it looks like RHB, but if you separate out R into 1 and 2 (although it doesn’t look exactly like a 2), and separate out B into 1 and 3, then you end up with this:

12H13

H looks a bit like 1 – 1, and if you add that to what you already have, you will end up with:

121-113,

which is 8.

Logic Puzzle 3/50

PUZZLE 3

This puzzle is another one of my own design. It concerns seven coins in a row on a table. Each of them was minted in a different year, and have varying values. The aim of the puzzle is to figure out the value, position in the row and year of minting of each coin. You have the following information:

1. The oldest coin is third from the right.

2. The coin on the extreme right is more than ten years older than the one on its immediate left.

3. The two five-rupee coins are next to each other.

4. The coin of the highest value is also the most recent.

5. The coin that is second from the left was minted in 1989.

6. The year of minting of the second coin from the left uses the same digits as the coin two spaces to its right.

7. The above also applies for the third coin from the left.

8. The extreme left and extreme right coins were both minted in palindromic years (palindromic numbers can be read from right to left as well as left to right and be read as the same number, such as 454 or the word ‘level’).

9. The second-oldest coin is worth two rupees.

10. The coin in the centre is of the lowest value.

Values: (all in rupees): 1, 2, 2, 2, 5, 5, 10

Years of minting: 1967, 1976, 1989, 1991, 1998, 2002, 2012

Solution to Puzzle 1

Consider A’s statement. If he is honest, then so is D. If he is dishonest, then D is of a different type; that is, honest. So, D must be honest.

His statement confirms that he eats fish, and that all of the others are dishonest.From C’s statement, it can be deduced that he eats chicken, and so A or B is vegetarian.

B cannot be honest; no honest person would claim to be a dishonest vegetarian. Since he is dishonest, he cannot be a dishonest vegetarian either, or he would be telling the truth. Therefore, he must be a dishonest mutton-eater.

Therefore, the final answer is that A is the vegetarian, B eats mutton, C eats chicken and D eats fish.

Logic Puzzle Of The Week (2/50)

This week’s puzzle is from Professor Layton and the Lost Future, one of my favorite games. This puzzle appears relatively early in the game, and yet has tripped up many people whom I have asked. The solving time ranges from two minutes to eighteen hours. Rather than tell you my version, I’ll just quote the text directly.

“It seems you need to enter a number to open the door. The only clue you have is a hastily written note from a woman known for her poor handwriting.

Can you work out the number you need?”Image

Logic Puzzle of the Week (1/50)

This is the first of fifty logic puzzles which I will be posting here every week of 2013, apart from the first and last weeks.

One of your friends is organizing a dinner party for you and four other people. He has asked each of them what they would like to eat, but has received no understandable reply. He asks you to decipher their statements, in order to find out which one is vegetarian.

Known information:

One of the four people (let’s call them A, B, C and D) eats mutton (and no other meat), one eats only chicken, one eats only fish and one is entirely vegetarian.

Each of them is either honest, and can never lie, or dishonest, and can never tell the truth.

These are their statements.

A: D and I <as in myself, not another person named I> are of the same type <both honest or both dishonest>.

B: I am a dishonest vegetarian.

C: I do not eat meat beginning with the letter C.

D: The only honest one among us eats fish.

Which one is vegetarian?