3 girls: Ellie, Raven, and Lynn
3 boys: Bryan, Eric, and George
A) Children with an even number of letters in their names were standing on the odd-numbered steps of the staircase and children with an odd number of letters in their names were standing at the even-numbered steps.
Names with an odd number of letters: Ellie, Raven, Bryan
Names with an even number of letters: Lynn, Eric, George
B) The children were standing on the stairs numbered between 10 and 20.
Thus, the possible stair numbers are 12, 13, 14, 15, 16, 17, 18, 19.
The numbers of toffees are 50, 31, 35, 36, 30, and 57
1) The number of toffees with Ellie is an even number which is twice her stair number.
Number of toffees = 50 or 36 or 30
Stair number = 25 or 18 or 15
Using A, we can eliminate stair numbers 15 and 25.
| Stair Number | Names | Toffees |
|---|
| 12 | | |
| 13 | | |
| 14 | | |
| 15 | | |
| 16 | | |
| 17 | | |
| 18 | Ellie | 36 |
| 19 | | |
2) Ellie and George were standing at a gap of 4 steps and the difference in the numbers of toffees with them is 1.
Number of toffees with George = 35
Using B, stair number of George = 13
| Stair Number | Names | Toffees |
|---|
| 12 | | |
| 13 | George | 35 |
| 14 | | |
| 15 | | |
| 16 | | |
| 17 | | |
| 18 | Ellie | 36 |
| 19 | | |
3) The stair numbers of Bryan and Lynn are not prime numbers.
Stair numbers of Bryan and Lynn = 12, 14, 15, or 16
Using A, Bryan's stair number = 12, 14, or 16, and Lynn's stair number = 15
4) The number of toffees with Lynn is a multiple of her stair number.
Therefore, the number of toffees with Lynn = 30
5) Bryan is standing above George.
Therefore, Bryan's stair number = 12
| Stair Number | Names | Toffees |
|---|
| 12 | Bryan | |
| 13 | George | 35 |
| 14 | | |
| 15 | Lynn | 30 |
| 16 | | |
| 17 | | |
| 18 | Ellie | 36 |
| 19 | | |
6)The stair number of Eric is higher than the stair number of Raven by 5.
Raven's stair number = 14
Eric's stair number = 19
7) Raven has less than 50 toffees.
Number of toffees with Raven = 31
8) The second-highest number of toffees is that of Eric.
Number of toffees with Eric = 50
Therefore, the number of toffees with Bryan = 57.
| Stair Number | Names | Toffees |
|---|
| 12 | Bryan | 57 |
| 13 | George | 35 |
| 14 | Raven | 31 |
| 15 | Lynn | 30 |
| 16 | | |
| 17 | | |
| 18 | Ellie | 36 |
| 19 | Eric | 50 |
Rule 1: The person who had the highest number of toffees moved to step 1 of the staircase.
| Stair Number | Names | Toffees | New stair number |
|---|
| 12 | Bryan | 57 | 1 |
| 13 | George | 35 | |
| 14 | Raven | 31 | |
| 15 | Lynn | 30 | |
| 16 | | | |
| 17 | | | |
| 18 | Ellie | 36 | |
| 19 | Eric | 50 | |
Rule 2: The person whose number of toffees is a prime number moved below by 5 steps if it is not occupied. Otherwise, the person remained in his original position.
| Stair Number | Names | Toffees | New stair number |
|---|
| 12 | Bryan | 57 | 1 |
| 13 | George | 35 | |
| 14 | Raven | 31 | 14 |
| 15 | Lynn | 30 | |
| 16 | | | |
| 17 | | | |
| 18 | Ellie | 36 | |
| 19 | Eric | 50 | |
Rule 3: If the difference between the numbers of toffees with any two persons was a multiple of 10, then they swapped their positions.
| Stair Number | Names | Toffees | New stair number |
|---|
| 12 | Bryan | 57 | 1 |
| 13 | George | 35 | |
| 14 | Raven | 31 | 14 |
| 15 | Lynn | 30 | 19 |
| 16 | | | |
| 17 | | | |
| 18 | Ellie | 36 | |
| 19 | Eric | 50 | 15 |
Rule 4: The person whose number of toffees is a perfect square moved 10 steps above.
| Stair Number | Names | Toffees | New stair number |
|---|
| 12 | Bryan | 57 | 1 |
| 13 | George | 35 | |
| 14 | Raven | 31 | 14 |
| 15 | Lynn | 30 | 19 |
| 16 | | | |
| 17 | | | |
| 18 | Ellie | 36 | 8 |
| 19 | Eric | 50 | 15 |
Rule 5: The person whose stair number and the number of toffees are odd numbers remained in his original position.
| Stair Number | Names | Toffees | New stair number |
|---|
| 12 | Bryan | 57 | 1 |
| 13 | George | 35 | 13 |
| 14 | Raven | 31 | 14 |
| 15 | Lynn | 30 | 19 |
| 16 | | | |
| 17 | | | |
| 18 | Ellie | 36 | 8 |
| 19 | Eric | 50 | 15 |
Hence, Bryan had the highest number of toffees.