Solve the rebus: TIC+TAC=ACT. Letters are encoded numbers. The same letters mean the same digits, different letters mean different digits.

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Using each of the digits 1, 2, 3, 4 exactly twice, write an eight-digit number with exactly one digit between the ones, exactly two digits between the twos, exactly three digits between the threes, and exactly four digits between the fours.

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William, Oliver and James were solving problems. William said: "I have solved the most problems." Oliver doubted: "Either you didn't decide the most, or James decided the least." James said: "I've solved more problems than Oliver."
Who solved the most problems if only one of the boys is right?

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At the moment 1 dollar is worth 3 shekels 55 agorot.
How many dollars is 1 shekel worth?

ℹ️ A shekel is worth 100 agorot.
A dollar consists of 100 cents.
If the number of cents is not whole, it is rounded upwards.

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Five people took turns eating the cake. The first ate a fifth of it, the second ate a quarter of it, the third ate a third of the new leftover, the fourth ate half of what was left after the third, and the fifth finished the cake all the way.
Which one ate the most?

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There are 1,000 inhabitants of Cissylvania. Three of them are vampires, but few know which ones. A visiting writer, Mr. Stocker, asked each resident to name two people he thought were vampires. Each vampire named two other vampires, and the others could name whomever they wanted. Prove that, using the data from the survey (and knowing that there are exactly three vampires in Cissylvania), Mr. Stocker could choose a guide who is not a vampire.

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Seven teams participated in the one-round soccer tournament (each team played exactly one match against each other). At the end of the tournament, the top-ranked teams scored exactly half of the points. Could there have been exactly 6 draws at the end of the tournament? (3 points are given for a win, 1 for a draw and 0 for a loss).

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