Three travelers, Jano, Kira, and Lian set out from Zerathania visiting exactly two of the countries. Each country is visited by exactly two travelers. Each traveler has a unique Flight Cost, which represents the total cost of airfare in traveling to both the countries and back to Zerathania. The Flight Cost of Jano was 4000 Zentars, while that of the other two travelers were 5000 and 6000 Zentars, not necessarily in that order. When visiting a country, a traveler spent either 1000, 2000 or 3000 in the country's local currency. Each traveler had different spends (in the country's local currency) in the two countries he/she visited. Across all the visits, there were exactly two spends of 1000 and exactly one spend of 3000 (in the country's local currency).
The total “Travel Cost” for a traveler is the sum of his/her Flight Cost and the money spent in the countries visited.
The citizens of the four countries with knowledge of these travels made a few observations, with spends measured in their respective local currencies:
i. Aurevia citizen: Jano and Kira visited our country, and their Travel Costs were 3500 and 8000, respectively.
ii. Brelosia citizen: Kira and Lian visited our country, spending 2000 and 3000, respectively. Kira's Travel Cost was 4000.
iii. Cyrenia citizen: Lian visited our country and her Travel Cost was 36000. What is the sum of Travel Costs for all travelers in Zentars?
41000
Step-by-Step Solution
Key idea: This is a currency conversion and logical deduction puzzle, recognisable because travelers visit countries with different currencies, and costs are given in mixed units (local currency vs Zentars).
Step 1: Map Travelers to Countries.
- Aurevia: Jano, Kira.
- Brelosia: Kira, Lian.
- Cyrenia: Lian, Jano (since each country visited by exactly 2).
Step 2: Determine Local Spends.
Global Spend Counts: Two 1000s, Three 2000s, One 3000.
From Brelosia: Kira spent 2000 Brins, Lian spent 3000 Brins.
From Aurevia: Kira's spends must be different. She spent 2000 in Brelosia, so she must spend 1000 Aurels in Aurevia.
Remaining spends: One 1000, Two 2000s.
Lian's other spend (Cyrenia) must be different from 3000. Jano's spends must be different.
If Lian spent 1000 in Cyrenia, Jano would have to spend 2000 and 2000, violating the distinctness rule.
So Lian spent 2000 Crowns in Cyrenia.
Jano spent 1000 and 2000 in Aurelia/Cyrenia.
Step 3: Calculate Exchange Rates and Flight Costs.
Let A, B, C be values of 1 Aurel, Brin, Crown in Zentars. C = 0.5.
Kira's TC: 4000 Brins = 8000 Aurels => B = 2A.
Kira's FC in Brins + 2000 + 1000(A/B) = 4000 => FC_K(B) + 2500 = 4000 => FC_K(B) = 1500.
Lian's TC: 36000 Crowns. FC_L(C) + 3000(B/C) + 2000 = 36000.
Testing the discrete FC values (4000, 5000, 6000 Zentars):
If FC_K = 6000 Zentars, then 1500 * B = 6000 => B = 4. Since B = 2A, A = 2.
Then B/C = 4 / 0.5 = 8.
Lian's eq: FC_L(C) + 3000(8) + 2000 = 36000 => FC_L(C) + 26000 = 36000 => FC_L(C) = 10000.
FC_L in Zentars = 10000 * 0.5 = 5000. Valid!
So FC_K = 6000, FC_L = 5000, FC_J = 4000. Sum of FC = 15000.
Step 4: Sum all Travel Costs in Zentars.
Total TC = Sum(FC) + Sum(Spends in Zentars).
Kira Spends: 1000(2) + 2000(4) = 10000.
Lian Spends: 3000(4) + 2000(0.5) = 13000.
Jano Spends: 1000(2) + 2000(0.5) = 3000.
Total Spends = 26000.
Total TC = 15000 + 26000 = 41000.
Answer: 41000