Mental Sum

Question:
There are a total of 150 coins in 14 piggy banks. If each piggy bank contains a different number of coins, what is the largest number of coins that can be found in one of the piggy banks.


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My boy tossed this question to his daddy and his mommy during a car ride last weekend. We solved it mentally within 2 minutes. You can do it too, the key is practice.

Of course, there was trick invented by a Math wizard many, many years ago when he was just 5 years old or so. We taught our boys when they were around that age too.

Answer
Container 1 holds 1 coin;
Container 2 holds 2 coins;
Container 3 holds 3 coins;
...
Container 13 holds 13 coins;
Container 14 holds ??? coins


What is the sum of

1 + 2 + 3 + ... + 13 ?
Flip it the other way round,

13 + 12 + 11 + ... + 1
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14 + 14 + 14 + ... + 14

So the sum is 13*14/2 or 13*7 = 91
So ??? = 150-91 = 59 (Ans)