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Submitted by amh100 on Tue, 2012-02-28 17:17
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You have 5 bales of hay. for some reason, instead of being weighed individually, they were weighed in all possible...

You have 5 bales of hay. for some reason, instead of being weighed individually, they were weighed in all possible combinations of 2 bales: bales 1 and 2, bales 1 and 3, bales 1 and 4, bales 1 and 5, bales 2 and 3, bales 2 and 4, and so on. the weights of these combinations were writtin down and arranged in numerical order, without keeping track of which weight matched which pair of bales. the weights in kilograms were: 80,82,83,84,85,86,87,88,90, and 91. your task is to find out how much each of the bales weighs.

Submitted by Andrein on Tue, 2012-02-28 19:50
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39,41,43,44,47 (Complete answer with step-by-step instructions)

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Since we have 5 xxxxx xx hay that means xx xxxx 10 different combinations. xxx in all xxxxx combinations we xxx xxxx bale xx hay xxxxxxx 4 times. xxxx xxxxx that xx we xxx up xxx xxx weights and xxxxxx xx 4 we will have the xxx xx xxx xxxxxxx xx xxxx xxxxxxxxxx bale.

80 x 82 x xx x 84 + xx + xx x 87 + xx x 90 x xx = 856 kg

xxxxx x 214 kg

xxx xx + b2 + xx x b4 + xx = 214kg

x

xxx xx xxxx over the measured weights xxx we xxxxxx xxxx xx xxxx have 4 odd numbers. xxxx xxxxx xxxx xxx xxxxx 4 measurements xx xxx an even xxx xx odd weight. xx at xxxxx 1 bale xxx xx xxx weight xxx xx least x bale xxx xx xxxx weight.

xx xxxx now xx xxx remaining xxxxx bales. xx one out xx xxx remaining 3 bales was different from the other two xxxxxxx xx xxxx 1 xxx and 2 xxxx xx x evens xxx x odd) xx would have 6 xxx xxxxxxxxxxxx in xxxxxx xx that means that xxx remaining 3 xxxxx xxxx xxx xxxx parity.

In xxxxxx we either have xxx bale with xx xxx weight xxx all xxx others with an xxxx xxxxxx or x xxxx with xx

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