Factory technician Ian has 10 batches of tires, all of which, but one, have tires weighing 100kg. One batch has tires weighing 90kg. Ian is allowed to use the scales only once. How can he spot the odd batch out?

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**Answer 1**

Take one tire from batch 1, two tires from batch 2, three tires from batch 3 etc. With 100 kg tires in all batches you get a weight of 5500 kg; now weighing the sample (as above described), then deduct this result from 5500 and divide by 10, the you get the batch with the 902 kg tires. Example: Batch 3 = 90 kg, the weight is 5470 kg 5500-5470 = 30 30/10 = 3 (= Batch 3)

**OR**

Leave batch 10 out. Then the same as below for batch 1-9, gives 45 tires to weight. When all batches have 100 kg tires, then you get a total of 4500 kg; if there is any difference to 4500 kg after weighing all 45 tires, then deduct the result from 4500 kg, divide by 10 and we get the number of the batch. If not, it is batch 10 with the 90 kg tires.

*Hans-Bernd Lüchtefeld**, market research & communication manager, PHP Fibers GmbH, Germany*

**Answer 2**

He places 1 tire from batch 1 along with 2 tires from batch 2, 3 tires from batch 3, 4 tires from batch 4, 5 tires from batch 5, 6 tires from batch 6, 7 tires from batch 7, 8 tires from batch 8, 9 tires from batch 9 and 10 tires from batch 10.

If the total weight is 5,490kg, then batch 1 is the odd one

If the total weight ends in 5,480Kg, then batch 2 is the odd one

If the total weight ends in 5,470Kg then batch 3 is the odd one

If the total weight ends in 5,460Kg then batch 4 is the odd one

If the total weight ends in 5,450Kg then batch 5 is the odd one

If the total weight ends in 5,440Kg then batch 6 is the odd one

If the total weight ends in 5,430Kg then batch 7 is the odd one

If the total weight ends in 5,420Kg then batch 8 is the odd one

If the total weight ends in 5,410Kg then batch 9 is the odd one

If the total weight is a multiple of 5,400Kg then batch 10 is the odd one

*John Droogan**, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK.*

**Answer 3**

I am not sure If “using” the scale once includes reading the result several times but I would pile all 10 batches on top of each other and then remove one by one. When the number can be divided by 100 without digit after the comma, the previous batch had 90 kg.