Suppose you have a set of cards numbered consecutively from 1 to 100. You try to put the cards in pairs so that the sum of the of the numbers on the cards in each pair is 94. How many pairs will you have?
2007-10-13 07:12:33 · 4 answers · asked by the flyer 1 in Science & Mathematics ➔ Mathematics
x+y=94, 1+93, 46,1 to 46, 48-93, 46.using 92 cards. Not 47, not 94-100. Logic dictates that to maximize the number of pairs(2) You take from the first half and add to the second half. Since 94/2 is a unique number, that cannot be part of the pairing.
2007-10-13 07:37:32 · answer #1 · answered by Wylie Coyote 6 · 1⤊ 0⤋
Since you have no cards with negative numbers and no card numbered zero, you will first have to set aside all cards numbered 94 and higher. Of the remaining 93, start pairing those at each end--i. e. 1 and 93, then 2 and 92, etc. At the end, you wil have 46 pairs and, since you started with an odd number, one (#47) left over.
2007-10-13 14:43:35 · answer #2 · answered by aida 7 · 0⤊ 0⤋
Well, since half of 94 is 47, after 47, the pairs will start to repeat each other. So, you'll have 47 pairs
But, you have to take out the last pair of 47 - 47 because you will only have one 47 card in the stack.
So, you'll have 46 pairs of cards that add to 94.
2007-10-13 14:23:56 · answer #3 · answered by its_victoria08 6 · 0⤊ 1⤋
If you have 100 cards, then you'll have 50 pairs. It doesn't matter what's on the cards. A pair is two cards, and 100/2=50
2007-10-13 14:21:36 · answer #4 · answered by International Socialite 3 · 0⤊ 2⤋