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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
Exeter Book Riddle 7; Exeter Book riddle 9; Exeter Book Riddle 12; Exeter Book Riddle 24; Exeter Book Riddle 25; Exeter Book Riddle 26; Exeter Book Riddle 27; Exeter Book Riddle 30; Exeter Book Riddle 33; Exeter Book Riddle 44; Exeter Book Riddle 45; Exeter Book Riddle 47; Exeter Book Riddle 51; Exeter Book Riddle 60; Exeter Book Riddle 61 ...
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.
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]
In this case, the term following 21 would be 1112 ("one 1, one 2") and the term following 3112 would be 211213 ("two 1s, one 2 and one 3"). This variation ultimately ends up repeating the number 21322314 ("two 1s, three 2s, two 3s and one 4"). These sequences differ in several notable ways from the look-and-say sequence.
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.
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