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Because the census taker knew the total (from the number on the gate) but said that he had insufficient information to give a definitive answer, there must be more than one solution with the same total. Only two sets of possible ages add up to the same totals: A. 2 + 6 + 6 = 14 B. 3 + 3 + 8 = 14
Four fours is a mathematical puzzle, the goal of which is to find the simplest mathematical expression for every whole number from 0 to some maximum, using only common mathematical symbols and the digit four.
A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge.In a puzzle, the solver is expected to put pieces together (or take them apart) in a logical way, in order to find the solution of the puzzle.
The misdirection in this riddle is in the second half of the description, where unrelated amounts are added together and the person to whom the riddle is posed assumes those amounts should add up to 30, and is then surprised when they do not — there is, in fact, no reason why the (10 − 1) × 3 + 2 = 29 sum should add up to 30.
[2], pp. 26–27; [11] It has been given the index number H506.3 in Stith Thompson's motif index of folk literature, and is ATU 1579 in the Aarne–Thompson classification system. [12] The puzzle was a favorite of Lewis Carroll, [13] and has been reprinted in various collections of recreational mathematics. [2], p. 26.
The Hardest Logic Puzzle Ever is a logic puzzle so called by American philosopher and logician George Boolos and published in The Harvard Review of Philosophy in 1996. [1] [2] Boolos' article includes multiple ways of solving the problem.
Alternatively, the prisoners build two groups of 5. One group assumes that the number of red hats is even, the other assumes that there is an odd number of red hats. Similar to the variant with hearing, they can deduce their hat color out of this assumption. Exactly one group will be right, so 5 prisoners answer correctly and 5 do not.
The equality of the two geometric sequences can be stated as the equation (2 0 + 2 1 + 2 2)(7 0 + 7 1 + 7 2 + 7 3 + 7 4) = 7 1 + 7 2 + 7 3 + 7 4 + 7 5, which relies on the coincidence 2 0 + 2 1 + 2 2 = 7. Note that the author of the papyrus listed a wrong value for the fourth power of 7; it should be 2,401, not 2,301.
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