Could you explain that what does it calculate or solve during mining(doing calculating/solving algorithms or math questions) since it is a supercomputer.
Well, it solves the user provided proof-of-work algorithms. They can be anything and they are programmed in elastic's own programming language ElasticPL.
One example it to use ElasticPL to mine other blocks (of different cryptocurencies).
Mining Bitcoin block #0 (the genesis block) could be done this way:
(Note: m[22] is the nonce which is meant to be found, the rest is the blockheader and some mandatory ElasticPL overhead)
input 3;
m[3]=16777216;
m[4]=0;
m[5]=0;
m[6]=0;
m[7]=0;
m[8]=0;
m[9]=0;
m[10]=0;
m[11]=0;
m[12]=1000599037;
m[13]=2054886066;
m[14]=2059873342;
m[15]=1735823201;
m[16]=2143820739;
m[17]=2290766130;
m[18]=983546026;
m[19]=1260281418;
m[20]=699096905;
m[21]=4294901789;
m[22]=m[1];
SHA256 3 80;
SHA256 3 32;
verify (m[10]==0);
The "bounty submissions" are defined by the last line, so the scientist only gets solutions meeting this criteria,
and the POW hash is more complicated and involes the state and the random input to get unique hash value which must meet a certain target value.