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From the sum and the product, it is easy to know the individual numbers and thus he tells Sue that "Now I know X and Y". Pete is now done and exits the game. Sue and Otto recalculate Table 1, this time only counting products of 2-splits from sums that are in Table 2 instead of from all numbers in the range 5 to 100 as in the original Table 1.
Flow of dollars in the riddle – comparing the sum of values circled in yellow (10+10+10=30) with the sum of absolute values of those shaded yellow (9+9+9+2=29) is meaningless. The missing dollar riddle is a famous riddle that involves an informal fallacy. It dates to at least the 1930s, although similar puzzles are much older. [1]
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
An impossible puzzle is a puzzle that cannot be resolved, either due to lack of sufficient information, or any number of logical impossibilities. 15 Puzzle – Slide fifteen numbered tiles into numerical order. It is impossible to solve in half of the starting positions. [1]
Because Bernard (who knows the bus number) cannot determine Cheryl's age despite having been told this sum, it must be a sum that is not unique among the possible solutions. On examining all the possible ages, it turns out there are two pairs of sets of possible ages that produce the same sum as each other: 9, 4, 4 and 8, 6, 3, which sum to 17 ...
Constant sum: A game is a constant sum game if the sum of the payoffs to every player are the same for every single set of strategies. In these games, one player gains if and only if another player loses. A constant sum game can be converted into a zero sum game by subtracting a fixed value from all payoffs, leaving their relative order unchanged.
For example, if the clue is 6 2 3, this step produces the sum 6 + 1 + 2 + 1 + 3 = 13. Subtract this number from the total available in the row (usually the width or height of the puzzle). For example, if the clue in step 1 is in a row 15 cells wide, the difference is 15 - 13 = 2.
17 indivisible camels. The 17-animal inheritance puzzle is a mathematical puzzle involving unequal but fair allocation of indivisible goods, usually stated in terms of inheritance of a number of large animals (17 camels, 17 horses, 17 elephants, etc.) which must be divided in some stated proportion among a number of beneficiaries.