Every validator sends just 1 secret number.
So we have 2000 validators with all the same deposit amount, every validator sends in 1 secret number before epoch 10N. 100 numbers are used in epoch 10N, 100 numbers are used in epoch 10N+1, … ,100 numbers are used in epoch 10N+9. A secret number is only used once, so we have used a total of 1000 numbers in 10 epochs. The other 1000 will not be used. Before epoch 10N+10 we have received 2000 new secret numbers and we start over.
So only 5% of the validators will get a block in an epoch. This is not enough to reach finality if we are using blocks as votes, so we will need to use the current Casper scheme or something like you proposed in this post:
“When a block is created, a random set of N validators is selected that must validate that block for it to be possible to build another block on top of that block. At least M of those N must sign off.”
For simplicity I used equal deposits, but we can allow validators with bigger deposits to send multiple secret numbers. These numbers must off course be send in different transactions for them to be unlinkable.