The workplace Dragoon has a problem. He wants to make mutants with Power Sweetie Extract. Aerallies need three times as many ounces of Power Sweetie Extract as Pussyfish to mutate, and twice as much syrup as Skimlets. Nurnies need half as many ounces to mutate as three ounces more than the number of ounces Aerallies need.
So anyway (where was I) - the Pets start coming into the mutation chamber and arrange themselves in a seven by seven grid in front of their feeding trough. The grid has a number on each square, like shown in the table below. Only one pet stands on each square.
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35
36 37 38 39 40 41 42
43 44 45 46 47 48 49
Pussyfish just LOVE prime numbers (didn't you know that?) so they run straight to the appropriate squares. Aerallies just love to get one-up on the Pussyfishes, so they all run straight to all the available squares below the Pussyfishes (ie. if a Pussyfish was in 28, the Aerally would occupy 35).
Two Nurnies then run to occupy spaces 4 and 6, and the rest of the Nurnies occupy every other square that is a multiple of those numbers. Skimlets then occupy the remaining squares.
The workplace master then takes a perfectly hemispherical spoon, 3 centimeters in radius, and starts transferring the syrup into the trough. Every single time he does this he only fills the ladle up to a depth of 2 centimeters while holding the ladle perfectly level. The first Pet to drink is a Pussyfish who, after drinking two ounces, mutates instantly.
My question is :
If the extract weighs 0.2 ounces per cubic centimeter, to three decimal places, how many ladles of syrup will the workplace master need to put into the feeding trough in order to mutate every Pet?
This weeks price is:
