Maximum number of weighing required to identify defective Wallets There are $10$ wallets and each wallet has Ten coins. In $8$ of the wallets each coin weighs $10$gm. But there are two defective wallets where in each coin weighs $11$gm. If we are allowed to use a Digital weighing machine, Find maximum number of Displays or Weighing Required to figure out two defective wallets. Assume all coins are identical.
My try:
I will arrange the wallets in a row and number the wallets from left to right as $w_1,w_2,w_3,\cdots,w_{10}$ 
From $w_1$ i will Collect one coin
From $w_2$ i will collect two coins
From $w_3$ i will collect three coins
$\vdots$
From $w_{10}$ i will collect all Ten coins.
This whole collection i will place it on the digital machine. If at all there are no defective wallets then the machine will show the weight as:
$$x=10+20+30+\cdots+100=550$$
But Since there are two defective wallets and we are collecting at least one coin from each wallet the weight shown is more than $x$
Case $1.$ If the weight shown is $x+3$ Then evidently the defective wallets are $w_1,w_2$ Since $3$ can be partitioned as sum of two order independent distinct positive integers as $3=1+2$
Case $2.$ Like wise if the weight shown is $x+4$ then $w_1,w_3$ are defective wallets.
Similarly if the weight is $x+19$ and $x+18$ then $w_9,w_{10}$ and $w_8,w_{10}$ are the defective wallets respectively.
So in all the above just two displays will suffice.
So if we use this Partition logic the maximum number of partitions required is for $11$ as 
$$11=1+10=2+9=3+8=4+7=5+6$$ 
Hence Max number of weighing required is $FIVE$
Let me know is this a valid reasoning?

Nice idea to take different amount of coins from different bags. After first measurement, You will have at most 5 suspected pairs as You mentioned.
Hint: if You take $i$ coins from the $i$ - th pairs and weigh them together, You will be able to tell which pair is defective. That means only TWO weighings
Edit: it does not need to be any specific number from the pairs. as long as you take different amount from different pair
