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Regular readers of our newsletter will already be familiar with OFF AIR!, the section dedicated to conundrums and puzzles. By popular demand, we have decided to include some of our most popular puzzles here. To view the puzzles, click on the links below. When you think you know the answer, click on "View solution" to check. So get ready to exercise those grey cells and have fun! If you would like to submit an idea for a puzzle, please contact This e-mail address is being protected from spambots. You need JavaScript enabled to view it . We will give you a bottle of champagne if it is published in ON AIR!. Emergency exit PUZZLES
Dave, the concierge of an apartment building, notices that the pressure of the boiler is rising, and it will shortly explode. He phones two of the residents, tells them the news, asks them to do the same and phone just two more (new) people, and then get out of the building. Assume that each of the residents is in and answers the phone immediately. If each phone call takes 30 seconds, and it takes each person 90 seconds to get out of the building, how long will it take to empty all 375 apartments?
A sailor 1000 miles from land has become sick and needs medicine immediately. Luckily a number of identical planes are available, but they are only capable of carrying enough fuel to go 1000 miles and the owner won't sacrifice a plane for the mission. Assuming the planes can refuel each other instantaneously in flight, how can the sailor be saved without sacrificing any planes? How many planes will it take?
Alex was paddling his canoe upstream at a constant rate. After 6 miles, the wind blew his hat into the stream. Thinking that he had no chance to recover his cap, he continued upstream for 6 more miles before turning back. He continued rowing at the same rate on his return trip and over took his cap at exactly the same spot where he began his journey, 8 hours earlier. What was the velocity of the stream?
On Bagshot Island, there is an airport. The airport is the homebase of an unlimited number of identical airplanes. Each airplane has a fuel capacity to allow it to fly exactly 1/2 way around the world, along a great circle. The planes have the ability to refuel in flight without loss of speed or spillage of fuel. Though the fuel is unlimited, the island is the only source of fuel. What is the fewest number of aircraft necessary to get one plane all the way around the world assuming that all of the aircraft must return safely to the airport? How did you get to your answer? Notes:
Find the next line of this series: 1
Move 1 match to make a valid equation from the matches below (inequalities are not allowed).
Move three matches to make four squares (no more or less) of equal size in the picture below. You must use all the matches.
Two people check in their luggage before a flight. The first person finds that he has to pay £105 for excess weight and the second person has to pay £255. If only one person had checked all the luggage in, the excess weight charge would have been £780. The combined weight of the luggage is 80kg. How much weight of luggage is each passenger allowed without charge?
You have two pieces of string and a box of matches. Each piece of string takes 1 hour to burn from end to end. The pieces of string do not necessarily burn at constant rates. This means that if you light one then after half an hour it will not necessarily have burnt half the string. All you know is that after an hour the whole string will have burnt. How do you time an interval of 45 minutes by burning the strings?
Four beleaguered consultants are on one side of a bridge that they need to cross. It is dark, they only have one flashlight, which must travel with them as they cross. To add to their troubles, the bridge is weak, and will only support two people at a time. Hans can walk across in 1 minute. If Hans goes with Anne, it takes 2 minutes for them to cross. If Anne goes with Pierre, it takes them 10 minutes. The flashlight cannot be thrown, instead it must be carried and delivered from person to person. The four consultants are trying to make it across in time to make an important dinner engagement, and they only have 17 minutes to do it. How do they make it?
Shown below are 4 consultants buried up to their necks in the ground. They cannot move and can only look forward. Between A and B is a brick wall which cannot be seen through. They know that between them are 4 hats, 2 black and 2 white, but they do not know which colour they are wearing. In order to avoid being shot one of them must call out to the executioner the colour of their hat. If they get it wrong, everyone will be shot. They are not allowed to talk to each other and have 10 minutes to fathom it out. One of them calls out after 1 minute. Which one is it and why is he 100% certain, before he calls out, of the colour of his hat? There are no outside influences or other ways of communicating. They cannot move and are buried in a straight line.
SOLUTIONS
It will take 7 minutes to empty all 375 apartments. Here's why:
The number of residents informed in each time period is as follows: 1, 2, 3, 5, 8, ...
It will take 3 planes to save the sailor. All 3 planes, piloted by Alex, Bob, and Charlie, take off together with full tanks of gas.
The velocity of the stream was 1.125 mph. Here's why:
The fewest number of aircraft is 3! Imagine 3 aircraft (A, B and C). A is going to fly round the world. All three aircraft start at the same time in the same direction. After 1/6 of the circumference, B passes 1/3 of its fuel to C and returns home, where it is refuelled and starts immediately again to follow A and C. C continues to fly alongside A until they are 1/4 of the distance around the world. At this point C completely fills the tank of A which is now able to fly to a point 3/4 of the way around the world. C has now only 1/3 of its full fuel capacity left, not enough to get back to the home base. But the first "auxiliary" aircraft reaches it in time in order to refuel it, and both "auxiliary" aircraft are the able to return safely to the home base. Now in the same manner as before both B and C fully refuelled fly towards A. Again B refuels C and returns home to be refuelled. C reaches A at the point where it has flown 3/4 around the world. All 3 aircraft can safely return to the home base, if the refuelling process is applied analogously as for the first phase of the flight.
Each line describes the previous one, so line 9 is 13 (one 3), then 21 (two 1s), then 13 (one 3) etc etc. Therefore the correct answer for line 10 is 13211311123113112211.
The solution is 28kg as follows: C = price per kg for excess baggage 1) c(x - z) = 105 1) and 2) c(x + y - 2z) = 360 (80-z)/(80 - 2z) = 780/360
Take the first piece of string and light both ends. At the same time light one end of the second piece of string. When the two flames on the first piece of string meet - thirty minutes will have elapsed. When this happens, light the remaining unlit end of the second string and when the two flames on the second string meet a total of 45 minutes will have elapsed.
The two fastest walkers, Hans and Anne go across first (2 mins), Hans returns with the flashlight to the others (1 min). Then he remains on the wrong side of the bridge while the two slowest walkers, John and Pierre cross (10 mins). They hand the flashlight to Anne who goes back to the wrong side of the bridge (2 mins), picks up Hans and they cross together quickly to the right side (2 mins): total = 17 mins.
C calls out first. The reason? C can see B's white hat. He knows that if he is also wearing a white hat, then D would see two white hats, and would therefore call out. Since D has said nothing, B and C's hats must be different, and C knows he must be wearing a black hat. |
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