Table with four coins
A square table has a coin at each corner. Design an execution sequence, each of whose steps consists of one of the following operations:
- ONE: The operation chooses a coin (possibly a different one with each execution of the operation) and flips it.
- SIDE: The operation chooses a side of the table and flips the two coins along that side.
- DIAG: The operation chooses a diagonal of the table and flips the two coins along that diagonal.
such that at some point during the execution (not necessarily at the end), a state where all coins are turned the same way (all heads or all tails) obtains.
There are 3 types of configuration possible:
(a) all coins have same face up
(b) 3 coins have same face up (and 1 has the other face up)
(c) 2 coins have same face up (and other 2 have the other face up)
Config (a) is the desired final position. Configs (b) and (c) arepotentially one step away from the final position F (where all coins have same side facing up). However, is there a config such that we can choose one of O, S or D and then we are guaranteed to reach the final desired position F ? Yes, there is. A special case of config (c) where the diagonally opposite coins have same face up is such a penultimate position:
H T T H
T H or H T
Applying the D operation here will definitely result in F.
Perhaps our goal then should be to reach this position F’ from other positions.
If two coins along a side have same face up, then F can be reached through F’ by the following sequence: S, D.
Therefore, F can be reached from config (c) by the following sequence:D, S, D.
If a single coin is face up, then we have the following sequence towards F: O, D, S, D.
Applying this sequence to config (b) will definitely lead to F. Applying this sequence to config (c) however might result in config (b). Therefore this sequence must be repeated:
O, D, S, D, O, D, S, D.
This is the desired sequence of operations which will guarantee that the final position F is reached at some time during its execution.
More puzzles to try-
- Correct the equation by moving one matchstick 34+89=400 As given in the matchstick equation (34+89=400) in the above diagram, move ...Read More »
- 3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »
- Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »
- There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »
- Dr.Willam wants to operate for three different persons who were wounded. But he had only two surgical gloves. There is ...Read More »
- Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »
- In the gear arrangement, To which one will the needle touch, 1 OR 2Read More »
- A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »
- Which letter replaces the question markRead More »
- A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »
- A bridge will collapse in 17 minutes. 4 people want to cross it before it will collapse. It is a ...Read More »
- In a country where everyone wants a boy, each family continues having babies till they have a boy. After some ...Read More »
- A devotee goes to three temples, temple1, temple2 and temple3 one after the other. In front of each temple, there ...Read More »
- There is a perfectly accurate analog watch with hour, minute, and second hands. How many times a day do all three ...Read More »
- Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »
- Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »
- A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »
- In the middle of the confounded desert, there is the lost city of “Ash”. To reach it, you will have ...Read More »
- Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »
- Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »