Answer:
11
Explanation:
If each letter represents a digit, and digits are possibly repeated, you want to know the number of possible values of HELPS such that FLU+SHOT=HELPS.
Carry
The addition of two single decimal digits must necessarily result in a sum with a value from 0 to 18. That is, the carry from the sum can only be 0 or 1.
If two decimal numbers are added, the carry from one column to another cannot ever by 2, as the maximum sum of any column of digits is 19, when the carry from the previous column is considered.
These facts tell us that H=1, S=9, E=0, and the sum F+H ≥ 10.
FLO
Already we know that H=1, so F+H ≥ 10 means F=9.
For F+H = 10, the carry from L+O must be 0. The value of L will be 0, so P=O may be any of 10 values, 0–9. HELPS will be 10009–10099.
For F+H = 11, the carry from L+O must be 1. The value of L will be 1, and we require L+O = 10. That is, O=9. HELPS will be 10109.
HELPS can be any of 11 possible values: from 10009 to 10099, and 10109.