Problematics | Dollars and paise
This week, a currency puzzle that shows you how to spend a little over $5 and still keep all your money
When pioneering puzzler Mukul Sharma died some years ago, his friend Pritish Nandy, who had launched Sharma’s Mindsport column in The Illustrated Weekly of India in the 1980s, observed that any puzzle works when they are packaged well. It’s the story around the puzzle that is paramount; in addition, Sharma’s irreverent writing style was out of this world.
What we can infer from Nandy’s observation is that easiness or difficulty is incidental. The puzzle I have crafted below is somewhat on the easier side, but if you find solving it a fun experience, that should be all that matters.
# Puzzle 177.1
Five years ago, a friend of mine went on a work trip to the United States. Since it was a paid trip lasting only a few days, he decided to limit the amount of cash he was going to carry; he knew he could use his credit card should any unexpected expenses come up. For cash, he simply exchanged ₹2000 at the then rate, asking the bank to give him all the dollars in one-dollar bills and all the cents in one-cent coins.
As expected, he spent very little, choosing not to bring any gifts for his family or me. His entire expenses came to $5.35, but he never told me what he had spent it on. What he did tell me as a puzzler was that the number of dollar bills he had remaining was half the original number of one-cent coins he had collected at the bank. The number of cents he had remaining, on the other hand, was one-third the number of dollar bills he had collected originally.
{{/usCountry}}As expected, he spent very little, choosing not to bring any gifts for his family or me. His entire expenses came to $5.35, but he never told me what he had spent it on. What he did tell me as a puzzler was that the number of dollar bills he had remaining was half the original number of one-cent coins he had collected at the bank. The number of cents he had remaining, on the other hand, was one-third the number of dollar bills he had collected originally.
{{/usCountry}}It did not seem enough of a puzzle then, so I forgot all about it. Then he brought up the matter unexpectedly a few days ago. “Remember the money I exchanged before going to the US five years ago?”
{{/usCountry}}It did not seem enough of a puzzle then, so I forgot all about it. Then he brought up the matter unexpectedly a few days ago. “Remember the money I exchanged before going to the US five years ago?”
{{/usCountry}}“Yes,” I said, “I remember you mentioned a couple of equations between dollars and cents collected and cents and dollars remaining.”
“All these years, I had forgotten to re-exchange the currency. I found the money recently and went to the bank, which gave me Indian currency at the current exchange rate. Luckily, they charged no fees, either five years ago or now.”
“How much did you get?” I asked.
“That’s the interesting thing,” he said. “I got ₹2000, which was exactly the amount I had exchanged originally. It means I did all my shopping without spending a single paisa — or cent.”
“But what exactly did you buy for $5.35?”
He still wouldn’t tell me.
How much was ₹2000 worth in US dollars on the two occasions he went to the bank?
#Puzzle 177.2
PURPLE ELEMENT IN TABLE AND CHAIR
The above is a combined anagram of three fairytale characters, two of them being single names (10 letters each) and one a two-word name (5 and 3 letters).
Can you unscramble all three names?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 176.1
Hi Kabir,
We form two groups of pair sums as follows: (Group-1: second + third, fourth + fifth, sixth + seventh, and second + eighth) and (Group-2: third + fourth, fifth + sixth, and seventh + eighth). In the second step, we subtract the sum of the three Group 2 numbers from the sum of the four Group 1 numbers. Dividing the result by 2 gives the second digit.
In the third step, the other digits are obtained in a straightforward manner as follows: (first + second) minus second gives first, (second + third) minus second gives third, (third + fourth) minus third gives fourth, (fourth + fifth) minus fourth gives fifth, (fifth + sixth) minus fifth gives sixth, (sixth + seventh) minus sixth gives seventh, and (seventh + eighth) minus seventh gives eighth.
— Professor Anshul Kumar, New Delhi
With eight equations for eight unknowns, there are multiple routes to the solution. Professor Anshul Kumar’s approach (matched by Kanwarjit Singh) is the most elegant among those received. This is also the same method that Martin Gardner describes, crediting the trick’s creator Royal Heath.
#Puzzle 176.2
Hi,
The Problematics reader was born in 1924. Her sister was born in 1912 (age 12 in 1924, matching the last two digits 12). Their grandmother was born in 1862 (age 62 in 1924, matching the last two digits 62).
They died on their 100th birthdays, the grandmother in 1962 and the sister in 2012. The reader’s current age is 102 (she turned 102 in the first week of January 2026).
— Ajay Ashok, New Delhi
***
Hi Kabir,
The Problematics reader is 102 years old. She lost her elder sister in 2012 and her grandmother in 1962. Out of curiosity, is this Problematics reader a regular solver ? If so, who's this incredible lady?
— Sabornee Jana, Mumbai
The reader is just a figment of my imagination, Sabornee. That said, there is no age limit on readers, and 102-year-old solvers are as welcome as younger puzzlers of any age.
Solved both puzzles: Professor Anshul Kumar (Delhi), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Ajay Ashok (Delhi), Sabornee Jana (Mumbai), Anil Khanna (Ghaziabad), Dr Sunita Gupta (Delhi), Vinod Mahajan (Delhi), Yadvendra Somra (Sonipat), YK Munjal (Delhi), Shri Ram Aggarwal (Delhi), Shishir Gupta (Indore)
Solved Puzzle #176.2: Dr Nitin Trasi (Sydney)