Thirteen boxes of different colors are stacked one above another in alphabetical order either from the bottom or from the top. Each box contains a different number of toffees, all multiples of 13, with the maximum number of toffees in any box being 169. The number of boxes above box J is equal to the number of boxes below it. There are two boxes between box J and the Pink colored box. Five boxes separate the Pink and Yellow colored boxes. The box containing 13 toffees is placed immediately below the Yellow colored box. The Black colored box is placed immediately above the Red colored box and immediately below the box containing 169 toffees. The number of boxes above the Red colored box equals the number of boxes below the box containing 13 toffees. The White colored box is placed immediately above the box containing 65 toffees and immediately below the box containing 104 toffees. The number of boxes between the boxes containing 13 and 52 toffees is equal to the number of boxes between the boxes containing 52 and 104 toffees. Two boxes are placed between the Blue colored box (which does not have 13 toffees) and the Green colored box, which is immediately below box J.

What is the sum of the toffees in the Blue and Green colored boxes?

Question

Thirteen boxes of different colors are stacked one above another in alphabetical order either from the bottom or from the top. Each box contains a different number of toffees, all multiples of 13, with the maximum number of toffees in any box being 169. The number of boxes above box J is equal to the number of boxes below it. There are two boxes between box J and the Pink colored box. Five boxes separate the Pink and Yellow colored boxes. The box containing 13 toffees is placed immediately below the Yellow colored box. The Black colored box is placed immediately above the Red colored box and immediately below the box containing 169 toffees. The number of boxes above the Red colored box equals the number of boxes below the box containing 13 toffees. The White colored box is placed immediately above the box containing 65 toffees and immediately below the box containing 104 toffees. The number of boxes between the boxes containing 13 and 52 toffees is equal to the number of boxes between the boxes containing 52 and 104 toffees. Two boxes are placed between the Blue colored box (which does not have 13 toffees) and the Green colored box, which is immediately below box J.

What is the sum of the toffees in the Blue and Green colored boxes?

Accepted Answer

**Solution:**

1. There are 13 boxes arranged alphabetically either from top to bottom or bottom to top.

2. Box J has an equal number of boxes above and below it, so J is exactly in the middle at position 7.

3. Two boxes are between J (position 7) and Pink, so Pink can be at position 4 or 10.

4. Five boxes are between Pink and Yellow, so if Pink is at 4, Yellow is at 10; if Pink is at 10, Yellow is at 4.

5. The box with 13 toffees is immediately below Yellow, so Yellow cannot be at the bottom.

6. Black is immediately above Red and immediately below the box with 169 toffees.

7. The number of boxes above Red equals the number of boxes below the box with 13 toffees.

8. White is immediately above the box with 65 toffees and immediately below the box with 104 toffees.

9. The number of boxes between the boxes with 13 and 52 toffees equals the number of boxes between the boxes with 52 and 104 toffees.

10. Two boxes are between Blue (which does not have 13 toffees) and Green, which is immediately below J (position 7). So Green is at position 8.

11. From the above, the positions of boxes and toffees are deduced as:
   - J at 7 with 65 toffees
   - Green at 8 with 52 toffees
   - Yellow at 10 with 13 toffees
   - Pink at 4
   - Blue at 1 (since two boxes between Blue and Green at 8 means Blue at 1)
   - White at 6 with 104 toffees
   - Black at 3 with 169 toffees
   - Red at 2

12. Now, sum of toffees in Blue and Green boxes:
   - Blue has 104 toffees
   - Green has 52 toffees

13. Sum = 104 + 52 = 156

**Answer:** 156

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