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Problematics | Cash transfer
How to move a stack of coins from one place to another while retaining the original order
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It has been 15 years since the 25p coin went out of circulation. While it was still in business, it was the face of a structural anomaly that prevailed in the Indian coinage system. In the 1970s, the 25p coin was 19mm in diameter, making it smaller than the 26mm 10p coins of the time. The 10p coins, in fact, were larger than the 24mm 50p coins too. In 1982, a new series of 10p coins measuring 23mm in diameter was issued, followed by smaller versions. But the 25p anomaly remained until the coin was phased out in 2011.
With paise coins no longer in circulation, rupee coins being used today by and large follow a simple relation between size and denomination: a larger coin usually means a higher value. The only departure from the pattern comes from the circular ₹10 and 12-sided ₹20 coins, both of which have the same diameter of 27mm, although the ₹20 coin is heavier. The full list: ₹1 (20mm, 3.09g) ₹2 (23mm, 4.07g), ₹5 (25mm, 6.74g), ₹10 (27mm, 7.74g), and ₹20 (27mm, 8.54g).
In the following puzzle, treat “larger” and “smaller” as adjectives relating to the weight of the coins. A ₹20 coin, therefore, is larger than a ₹10 coin.
#Puzzle 218.1
Take three tablemats, one green (Go; you start here), one amber (Pause) and the third red (Stop). On the green mat, place one coin each of ₹2, ₹5, ₹10 and ₹20 in that order from top to bottom ( ₹2 on top, ₹20 at the bottom). Your challenge is to transfer the coins to the red mat so that they end in the same order. The rules are:
(a) You may move only one coin at a time. (b) A coin may be placed on any of the three mats, but at no stage can a larger (heavier) coin be placed on top of a smaller (lighter) one. (c) The amber mat is an intermediate transit point where you may temporarily keep one or more coins.
This can be done in 15 moves: (1) ₹2 from green to amber, (2) ₹5 from green to red, (3) ₹2 from amber to red, (4) ₹10 from green to amber, (5) ₹2 from red to green, (6) ₹5 from red to amber, (7) ₹2 from green to amber, (8) ₹20 from green to red, (9) ₹2 from amber to red, (10) ₹5 from amber to green, (11) ₹2 from red to green, (12) ₹10 from amber to red, (13) ₹2 from green to amber, (14) ₹5 from green to red, (15) ₹2 from amber to red.
This describes every move one by one. Is there a way to determine the number of moves required without listing them? Yes — there is a simple formula.
Now suppose you start with five coins on the green mat, with a ₹1 coin placed on top of the four coins above. In how many moves can you transfer the whole stack to the red mat? Try to discover the general formula and show why it works.
#Puzzle 218.2
You have a 3-foot ruler with no markings. Using a measuring tape, you want to mark certain points on the ruler so that you can measure any integral number of inches from 1” to 36”.
What is the minimum number of marks required, and where must they be placed?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 217.1
Dear Kabir,
The eldest sister is the TV actress, the second eldest is the stage actress, and the youngest is the film actress. As none of the sisters talks about herself, the third statement ("The film actress is not the youngest") could not have been made by her. As any statement not made by the youngest sister is false, this statement is false. Therefore, this establishes that the youngest sister is the film actress.
The first two statements are such that either both are true or both are false. As the youngest sister has to make at least one of the other two statements (and she always speaks the truth), it means both the first two statements are true. Thus, the eldest sister is the TV actress and the second eldest is the stage actress.
— Yadvendra Somra, Sonipat
***
We can proceed by assuming that the first statement is correct. Then either the TV actress or the film actress is the youngest. But it cannot be the TV actress as it would mean that the second statement is by someone else and therefore has to be false. If the film actress is the youngest, the stage actress has to be the middle sister and the TV actress has to be the eldest. The first two statements are then true and given by the film actress, and the last one by either of the other two sisters and therefore false.
The same conclusion follows if the second statement is taken as true. The third statement cannot be true as it would lead to contradictions.
— Kanwarjit Singh, Chief Commissioner of Income-tax (retired)
#Puzzle 217.2
Hi,
Let a, b, and c be the inheritances of the three men be, and let d be the woman’s inheritance. Given:
a + d = 2(b + c)
b + d = 3(a + c)
c + d = 5(a + b)
These equations can be reduced to: b = 3a, c = 5a, and d = 15a. The four inheritances are therefore in the ratio 1:3:5:15, the last being the woman’s share.
— Ajay Ashok, New Delhi
Solved both puzzles: Yadvendra Somra (Sonipat), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Ajay Ashok (Delhi), Dr Sunita Gupta (Delhi), Shishir Gupta (Indore), Professor Anshul Kumar (Delhi)
Solved #Puzzle 217.1: Dr Vivek Jain (Baroda)
Solved #Puzzle 217.2: Anil Khanna (Fremont), YK Munjal (Delhi), Vinod Mahajan (Delhi)
