Miscellaneous Problems

Problem 25. I am thinking of a whole number in the range from 0 to 15, inclusive. You are allowed to ask me 4 yes or no questions, to which I will respond truthfully. Can you always guess my number in at most four such questions?

Problem 24. Suppose we arrange the five numbers 1,2,3,4,5 in each of the five squares so that the horizontal and vertical lines both add to 8. Which number must go in the middle square?

Problem 23. Fill in the numbers from 1 up to 5 in the five little circles, in such a way that in each triangle the given number is the sum of the numbers on the vertices. Which number appears in the shaded circle?

Problem 22. Can we find five even integers whose sum is 25?

Problem 21. What is the value of 1 + 2 + 3 + ··· + 7 + 8 + 9 + 8 + 7 + ··· + 3 + 2 + 1, where all of the integers from 1 through 9 and then back down to 1 are added together?

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