Sunday, March 29, 2015

Camel Race

The time had come when the father of two sons was to decide who would receive his fortune.
They both kneeled before the aged man as he spoke. "You will both race your camels to the nearest city. The owner of whichever camel arrives at the gates second will receive my fortunes."

Confused, both men rode their camels toward the city, step by step, as slow as they could. As luck would have it, the Great Sage was passing by. Seeing him, they pleaded for his wisdom.

"How might we resolve this such that it doesn't take the rest of our lives," said the first man.
"And yet it must be in a competitive manner," added the second. "Neither of us are willing to concede."

The Great Sage stroked his beard and shared his wisdom.

On hearing his advice, both men ran back to the camels and raced toward the city as fast as they could.

camel race logical riddle

What was the Great Sage's suggestion?

Camel Race Puzzle Solution

The Great Sage told them to swap camels. It is the second camel, not person, to reach the city gates who wins.

Tuesday, March 24, 2015

Sherwood Forest

"A three-way duel is an old tradition in these lands," said Robin Hood, "because it is unlikely that between two champions, there shouldn't come a third party in between, to show he is the bravest.

Miller, Allan-a-Dale, and Brother Tuck now battle like real thieves, and may the best win. Here are the crossbows, each of them with its own set of arrows. The three crossbows are all slightly different, and each set of arrows works only on the crossbow it was designed for. Unfortunately, only one set of arrows is flawless: a quarter of the set of arrows of the second crossbow is faulty, as is an incredible half of the third set. A faulty arrow is indistinguishable from a good one until it is shot. Now, go on, pick a straw, and let fate be fulfilled."

Robin Hood showed his clenched fist, from which three straws stuck out. Miller was the luckiest, having picked the longest straw, while Brother Tuck stared at his short straw with an expression of dread, for he knew full well that none of the three men would miss a target with a good arrow. "Well, Miller, here it is: the king of all crossbows. You have a 100% chance of killing your target. Allan-a-Dale, I hand you the crossbow with a few faulty arrows: with it, your chances are 75%. And there you are, Brother Tuck: the 50% crossbow. But then, a religious man like you could even duel with only your spiritual belief."

The fit monk breathed deep, and muttered, "God almighty, Robin, you want to see me dead. It is not possible to duel in these conditions."

"You are right, Brother Tuck," replied Robin Hood, after thinking for a little while. "Here is what we will do. You, Brother Tuck, will have the right to shoot first, after choosing your desired position on the field. Friends, please remember the rules: you will take position on the corners of an imaginary triangle, each of you 80 yards away from the other two. The order in which you will take turns to shoot is clockwise. On your turn, you may choose which of the other two you wish to shoot. Get ready: it is time to duel!"

Brother Tuck gulped as he chose his position, a taunting raven fluttering overhead squawking songs of doom.
sherwood forest
What position (A or B) did Brother Tuck choose, and which adversary did he shoot first, in order to have the highest chance of survival?

Sherwood Forest Puzzle Solution

Since the order of turns was clockwise, Brother Tuck went to position B, and deliberately missed his firts shot (perhaps he should shoot the raven).

Assuming that missing the first shot gives Brother Tuck the best chance that one of the dangerous adversaries gets killed from the other before becoming himself the target (obviously, both Miller and Allan-a-Dale opt to use their first turn to shoot at the most dangerous adversary), it is necessary to consider the chances of shooting from position A and the chances from position B.

By assuming position at A, and missing the first shot (as it is right in the circumstances), Brother Tuck knows that he wouldn't be Miller's target, because Allan-a-Dale is more dangerous. Allan-a-Dale would certainly be killed (Miller's crossbow has 100% chances of hitting the target). At this point, it would again be the monk's turn (with Allan not being in a condition to take his turn), who has a 50% chance of hitting the other survivor, ie Miller, and to therefore end the duel. Obviously, if the religious man misses, then he could only get on his knees and pray, because Miller's next shot would be faultless. So, by choosing position A, Brother Tuck has a 50% chance of survival.

If Brother Tuck chooses position B, and deliberately misses his first shot, the next turn would be Allan-a-Dale's, who would choose the most dangerous adversary, ie Miller. At this point, two different outcomes can happen:

1. Allan misses Miller (25% chances); at this point, Miller will use his turn to shoot Allan. Then it will be Tuck's turn, who will have one chance out of two to pick one of the good arrows (so, it's 50% chances, but it's 50% of 25%, ie 1/8).

2. Allan hits Miller (75% chances); at this point, Brother Tuck will shoot Allan, with 50% chances of success; but this is 50% of 75%, ie 3/8 which, if added to 1/8 of the first outcome, gives Tuck 4/8, ie 50% chances of survival. In case that his shot misses, Tuck would not be a sure victim of Allan's next shot, who might miss with 25% chances. This gives the monk a further 3/32 probabilities (ie 3/4 * 1/2 * 1/4).

The calculation, as shown here, could keep going on and on until the last arrow, and demonstrates that, by choosing position B, Brother Tuck has, besides the 50% chances also offered by position A, a long string of small chances (3/32, 3/256, etc), that are possible if Allan-a-Dale misses at least one (his first, and eventually the next ones) shot at the monk.

Thursday, March 19, 2015

Golf

Jack, Levi, Seth, and Robert were, not necessarily in this order, a Stock Broker, a Musician, a Doctor, and a Lawyer. They drove, also not necessarily in order, a Porsche, a Ferrari, a Cadillac, and a Corvette.

The Stock Broker, was remarking to no one in particular one day, while finishing up a round of golf which involved all four friends, that he found it curious that Jack and the Lawyer each wanted to buy the Corvette, but that the Musician didn't because he preferred his Porsche. After the game was over, Seth offered to buy a round of sodas for the Doctor, for the owner of the Cadillac, and for the owner of the Corvette. Levi, who was beaten by the Stock Broker, was in a bad mood, and so he declined Seth's offer and left without joining the others in the club house.

What car did each person own, and what were their respective occupations

Golf Puzzle Solution

The clues given in the puzzle are:
  • The Stock Broker is not Levi.
  • Jack is not the Lawyer; neither Jack nor the Lawyer owns the Corvette.
  • The Musician owns the Porsche; therefore no one else owns the Porsche and the Musician owns no other car.
  • Seth is not the owner of the Cadillac, the Corvette, nor is he the Doctor; also, the Doctor does not own either the Cadillac or the Corvette either.
By Reasoning:
  • The Doctor, by elimination, must own the Ferrari; the Lawyer must own the Cadillac; the Stock Broker must own the Corvette.
  • Tne Stock Broker owns the Corvette. Neither Seth nor Jack own the Corvette, so the Stock Broker must be Robert; since the Stock Broker drives the Corvette, then Robert drives the Corvette.
  • The Lawyer owns the Cadillac. Seth does not own the Cadillac; therefore Seth is not the Lawyer; therefore Seth is the Musician; the Musician owns the Porsche; therefore Seth owns the Porsche.
  • By elimination, Jack is the Doctor; the Doctor owns the Ferrari; therefore Jack owns the Ferrari.
  • By elimination, Levi owns the Cadillac.
The Solution:
  • Seth is the Musician and owns the Porsche.
  • Levi is the Lawyer and owns the Cadillac.
  • Jack is the Doctor and owns the Ferrari.
  • Robert is the Stock Broker and owns the Corvette.

Saturday, March 14, 2015

Mountaineer

An Austrian mountaineer left Zurglatt, his village, at eight o'clock in the morning, and started his climb towards the refuge Tirpitz, on Gross Glossen mountain. He walked at a steady pace, without stopping, and his increase in heart pulse rate was negligible. He reached the refuge at three in the afternoon, i.e. seven hours since he left the village. At the refuge he rested, admired the view, scribbled some notes on his diary, sang three lieder, ate two sausages and drank a litre of beer. He then slipped into his sleeping bag and fell asleep.
mountaineer logical game

The next morning, at eight o'clock, he started his descent, again with a steady pace, but faster, since he was travelling downhill. He reached Zurglatt at one in the afternoon, after walking for five hours.

Could there be a point along the path where the mountaineer walked, on the outbound and the return journey, exactly at the same time of day?

Mountaineer Puzzle Solution

Of course there is. To make sure, imagine two mountaineers: one is in the village, and the other one is at the refuge. They'll both leave at eight o'clock, travel along the same path as our mountaineer, and at his same speed. At some point along the path they'll obviously meet.

Monday, March 9, 2015

General Manoeuvres

A platoon of 40 soldiers, inclusive of troopers, senior soldiers, sergeants and commander, was standing by the bank of a river. In order to cross it, they found only a small rubber rowing boat and a pair of paddles, belonging to two young boys. Due to its rather restricted size, the boat can only carry either the two boys together, or a single grown-up.

While the lieutenant - commander of the platoon - was trying to figure out the best way to organize the crossing, the radio received an urgent request: the captain wanted to know exactly how long the platoon would take to cross the river; ie how many minutes, or hours, or days were needed before the last man set his foot on the opposite bank of the river.

The lieutenant worked out that the boat, when carrying the two boys, would take 10 minutes to cross the river. One boy alone on the boat would need 5 minutes. One soldier - soldiers are not the best rowers - would take 8 minutes.

These calculations included the time taken by people to jump on board and get off the boat. After a few seconds, the officer, who had an above average IQ, sent the message with the answer to his captain.

How was the crossing organised, and how long did it take for the entire platoon to cross the river?


General Manoeuvres Puzzle Solution

The manoeuvre was conducted this way:
  1. The two boys cross to the opposite bank (10 mins)
  2. One of them stays there while the other comes back (5 mins)
  3. The boy gets off the boat, a soldier jumps on board and crosses the river (8 mins)
  4. The soldier gets off, and the boat returns with the other boy (5 mins)
This operation required 28 minutes. The sequence had to be repeated as many times as the number of men in the platoon, ie 39 more times. However, it was needed to subtract 5 minutes from from the total: when the last man of the platoon crossed, the time (5 mins) taken by the second boy to cross back must not be counted, as the last soldier had already reached the other bank of the river.

The total time was therefore [(28 * 40) - 5] = 1115 minutes, which amounts to 18 hours and 35 minutes.

Mike Horan points out that it can be done faster if you leave both boys stranded on one side with the boat on the other. The first 39 soldiers cross at 28 minutes each (1092 minutes). You then have the two boys plus the last solider on one side. The final soldier then rows across himself, hence 1092 + 8 = 1100 minutes.

Wednesday, March 4, 2015

Poker Results

poker game riddle
Alice, Barbara, Claire, Daniel and Edward are discussing the result of the card game of the previous night.

Person #1 (woman): "Claire is single. The sisters and brothers all together totalled a loss of £9."

Person #2 (man): "My wife and I have lost a total of £1."

Person #3 (woman): "My sisters-in-law, all together, have lost £2."

Person #4 (man): "My brother-in-law and I have managed to lose £12 all together."

Person #5 (woman): "My result combined with that of Alice - who is Daniel's wife and an only child - is overall positive."

How much has each of them won or lost?

Poker Results Puzzle Solution

The 5 people and their wins/losses are:

Person #1: Barbara (+ £4).
Person #2: Edward (- £5).
Person #3: Alice (+ £14).
Person #4: Daniel (- £7).
Person #5: Claire (- £6).

This result is obtained from the statements of the 5 people.
  • Since the sisters-in-law (#1 and #5) lost, wile #5 and Alice have won, then #3 is Alice.
  • Alice won £14, because £2 lost by the sister-in-law, and £12 lost by the men.
  • #1 is Barbara, as she talks about Claire.
  • Alice is the only child, therefore the sisters-in-law must be sisters of the husband (Daniel).
  • Daniel lost £7, as the bunch of brothers and sisters have lost a total of £9, of which only £2 was lost by the sisters.
  • Edward lost £5, as the two men lost a total of £12, of which £7 was lost by Daniel.
  • Barbara - Edward's wife because Claire is single - won £4, as the total lost by the couple Barbara-Edward is £1.
  • Claire lost £6, as the total loss of the two sisters is £2, but Barbara won £4.