Ajay explained, "I have put a hundred nuts in these five bags. In the first and second bags there are a total 43 nuts, in second and third bags...Read on...

## The five bags of nuts riddle

Ajay kept five bags on the table. He explained, "I have put a hundred nuts in these five bags. In the first and second bags there are a total of 43 nuts; in the second and third bags a total of 52 nuts, in the third and fourth bags a total of thirty and in fourth and fifth bags a total of thirty four."

How many nuts each bag had?

*Time to solve 5 minutes.*

With basic arithmetic and logical thinking, you should solve this riddle easily.

### Solution to the five bags of nuts riddle

The repeating pattern that caught my attention was the second, third and fourth bags appeared twice in the four pairs of bags mentioned.

Naturally, I concluded,

If I add the totals of the four pairs of bags, I will get total of all five bags, that is 100, plus total of the twice mentioned second, third and fourth bags.

The total of four pairs is: (43 + 52 + 30 + 34) = 159.

It follows, total of second, third and fourth bags is: (159 - 100) = 59.

I already know the total of second and third bags is 52. So,

The fourth bag contains, (59 - 52) = 7 nuts.

The rest are easy pickings:

- Total of third and fourth bags is 30 : the third bag contains (30 - 7) = 23 nuts.
- Total of second and third bags is 52 : the second bag contains (52 - 23) = 29 nuts.
- Total of first and second bags is 43 : the first bag contains (43 - 29) = 14 nuts, and,
- Total of fourth and fifth bags is 34 : the fifth bag contains (34 - 7) = 27 nuts.

All five together sum up to 100.

Identifying the odd pattern that the second, third and fourth bags appeared twice in the four pairs of bags mentioned was the key to this little riddle.

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