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Problematics | Sightseers’ route map
Two families use different routes to visit a town’s tourist spots. Some distances are given and some are not; can you fill in the gaps?
Bringing puzzles to a wide audience can sometimes bring unexpected rewards. Whether you create a new puzzle or adapt an existing one, readers can make observations that you had not noticed before. “The answer to your puzzle,” a reader or two occasionally may write to me, “has this interesting feature or that additional aspect.”
I am fortunate to have such observant readers. Obviously, one cannot use the new information for a new puzzle immediately after the original. But three years is long enough. I had presented one version of the following puzzle during the 2022 football World Cup, and at least one reader subsequently pointed out an aspect I hadn’t originally observed. In the new version, I have incorporated that aspect to create a puzzle that is a little more involved than the earlier version. The puzzle itself is not about football this time, and overall it should not be complicated even with the latest embellishment.
#Puzzle 166.1
Two families living in the same apartment go sightseeing to a nearby town, choosing separate hotels at the ends of the town’s Main Street. They start out together but take different routes. Family A takes a straight road from their apartment to Hotel A, a distance of 39 km. Starting from the same apartment, Family B takes a separate straight road to Hotel B. On the way, Family B passes one of the town’s main attractions, an amusement park, but decide not to stop.
Once they have reached their respective hotels, the two families call each other up. They realise that both their hotels are situated on Main Street, but 25 km apart.
In the morning, Family A decides to go first to the amusement park, which is 15 km from Hotel A. After spending some time amusing themselves, they travel to the town’s other attraction, a lake, which is 12 km from the park by a straight road. At the lake they run into Family B.
“So you came to the lake before the amusement park,” Husband A observes. “Yes,” says Husband B, “the lake is 16 km from our hotel, while the park is a longer distance.” Wife A asks, “When are you going back to your hotel?” to which Wife B replies: “We aren’t going back. We have checked out and will head home after visiting the amusement park.”
So Family A goes back to Hotel A, which is 9 km from the lake (straight road again). There they pack and head home the way they had come, which as you remember was a distance of 39 km.
Family B goes from the lake to the amusement park, a 12-km straight road already taken by Family A. Wife B notes once again that the park lies on the same straight road from their home city to Hotel B, and they could have stopped before checking into the hotel. Husband B argues that it was a decision well taken, because they can now go straight home from the amusement park.
There can be no answer to a couple’s argument between one decision and another. In any case, that decision has already been taken. But there is another question that we can definitely answer.
What is the distances (a) between the amusement park and Hotel B; and (b) between the amusement park and the couples’ home?
#Puzzle 166.2
OUR BEST NOVELIST, SENOR
This is an anagram I first came across more than 35 years ago, and the nice thing is that a Google search for the answer even today does not appear to yield instant answers. The anagram actually leads to a novelist, and the sentence “Our best novelist, Senor,” may be taken as a Scot proudly describing the long-deceased author to a Spanish gentleman being addressed as “Senor”. Yes, the novelist was Scottish and remains very popular, which should narrow your choices down, and his name consists of three words (6, 5, and 9 letters).
Unscramble the anagram.
MAILBOX: LAST WEEK'S SOLVERS
#Puzzle 165.1
Hello Kabir,
Say x is the number of dogs, y the number of cats, and z the number of mice. We have
3x + 1.5y + z = 20
x + y + z = 20
Solving for integer values,
(x, y, z) = (0, 10, 10), (2, 5, 13), (4, 0, 16)
Because we have all three pets (no zeros), the proper solution should be 2 dogs, 5 cats and 13 mice.
— Dr Sunita Gupta, Delhi
***
If X, Y, and Z are the numbers of dogs, cats and mice respectively,
3X + 1.5Y + 0.5Z = 20 ... (a)
X + Y + Z = 20 ... (b)
Multiplying (a) by 2 and subtracting (b), we get
5X + 2Y = 20
X cannot be 1 as Y would then be a fraction. So, the minimum value of X is 2. If we take that, then Y = 5. Putting these values in (b) we get Z = 13. Therefore, there are: 2 dogs (6 kibbles), 5 cats (7.5 kibbles) and 13 mice (6.5 kibbles). The total pets are 20, and the kibbles consumed also add up to 20.
— Kanwarjit Singh, Chief Commissioner of Income-tax, retired
#Puzzle 165.2
Hello Kabir,
The answer to the second puzzle is that the total length of the shark is 24 feet, with the head being 3 feet (given) and the trunk being 12 feet (one half the total length) and the tail being 9 feet (one half the trunk plus the 3-foot head). The total length of the shark fits within the original estimates of between 20 and 25 feet. The problem resolves to an algebraic equation (I won't include the work here) which is easily solved.
— Dr Jeffrey Geist, PhD, Columbus, Ohio
Solved both puzzles: Dr Sunita Gupta (Delhi), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Dr Jeffrey Geist (Columbus), Anil Khanna (Ghaziabad), Vinod Mahajan (Delhi), Sabornee Jana (Mumbai), Yadvendra Somra (Sonipat), Ajay Ashok (Delhi), YK Munjal (Delhi), Shishir Gupta (Indore)
Solved #Puzzle 165.1: Shri Ram Aggarwal (Delhi)
