Pure maths, physics, chemistry, etc.: brain-training tasks that have nothing to do with trade [Part 2] - page 36
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Hm... Well, one more clue. Everyone only has to flip a coin once to reach the goal.
It is possible to solve the problem without flipping a coin.
You need a coin and a napkin. Put a coin with the tails up and cover it with a napkin. All paranoiacs must take turns sticking their hand under the napkin and the one who paid for lunch (if there is one) must flip the coin.
After the third, the napkin is removed and the result is seen.
Since only one person can pay, there can't be two flips.
It is possible to solve the problem without flipping a coin.
You need a coin and a napkin. Put a coin with the tails up and cover it with a napkin. All paranoiacs must take turns sticking their hand under the napkin and the one who paid for lunch (if any) must flip the coin.
After the third, the napkin is removed and the result is seen.
Since only one person can pay, there can't be two flips.
Without flipping, but with a napkin.
Well, yes, the principle is exactly about parity. In the original solution, everyone flips a coin, but only the person on the right (and himself, of course) shows the result. Thus, everyone sees two coins: his own and his neighbour to the left. Afterwards everyone says whether they saw the same result (two heads or de tails) or different. If someone paid for lunch, he/she must lie. In the end, an even number of coincidences says that the one who paid is sitting at the table, an odd number says that the KGB is paying.
This solution is mathematically equivalent to yours, but it also illustrates the way in which an anonymous broadcast message can be transmitted on some network.
No tossing, but with a napkin.
Well, yes, the principle is exactly about parity. In the original solution, everyone flips a coin, but only the person to their right (and themselves, of course) sees the result. Thus, everyone sees two coins: his own and his neighbour to the left. Afterwards everyone says whether they saw the same result (two heads or de tails) or different. If someone paid for lunch, he/she must lie. In the end an even number of matches says that the one who paid is sitting at the table, an odd number says that the KGB pays.
This solution is mathematically equivalent to yours, but it also illustrates the way in which an anonymous broadcast message can be transmitted on some network.
(## / #) =(# - #) =(# + #) =(# / #)
Instead of grids, write the digits (123456789) so that all equalities are true. No digit should be used more than once.
(## / #) =(# - #) =(# + #) =(# / #)
Instead of grids, write the digits (123456789) so that all equalities are true. No digit should be used more than once.
56/8=9-2=3+4=7/1
bravo, sand! Here's another one:
Given a series of numbers: 1 2 3 4 5 6 7 8
Put punctuation marks between the digits so that the result is one. Calculations are done simply from left to right, without precedence.
Unfortunately, no. Your version gives a result of 10. Note the condition: "Calculations are just from left to right, without priorities."
I.e. 1+2=3, 3+3=6, 6*4=24, 24-5=19, etc.
That's right! The problem has 62 correct solutions, and this is one of them :)