1. The 10 test scores are 410, 420, 430, 440, 450, 460, 470, 480, 490, & 500 by Intro and Clue 1.

2. By Clue 8, the total of the scores on Row 1 is 230 = 5 * 46 points higher than the total of Row 2's scores. If the 1st 5 scores of the above list were on Row 2 and the last 5 on Row 1, then the difference would be 250. The only way to reduce the difference by 20 is to exchange one score for another 10 points higher, namely exchange 450 for 460. Therefore the scores of
   Row 2 must be 410, 420, 430, 440, & 460,
   and the scores of
   Row 1 must be 450, 470, 480, 490, & 500,
   in some order.

3. By Clue 7, 460 & 450 are in the same column.

4. By Clue 4 the scores in Col 1 add to 880. The only possibility remaining is 470, 410. Then by Clue 2, George sits in seat 10.

5. By Clue 1, Hugh sat in seat 7 and Ida in seat 8. The seating chart now looks as follows:

   		Column 1	Column 2	Column 3	Column 4	Column 5
   ROW 2	Name	6.	7. Hugh	8. Ida	9.	10. George
   	Score	410
   ROW 1	Name	1.	2.	3.	4.	5.
   	Score	470

6. From argument 3 above, 460 & 450 are in the same column. If this column is #5, then
   Sum of scores of Cols 2, 3, 4 = Sum of all scores - 880 - 910 = 2760 = 3x + 10 where x = Sum of scores of Col 2 = Sum of scores of Col 4 = (Sum of scores of Col 3) - 10 by Clue 6. The equation 2760 = 3x + 10 has no solution which is an integer. Therefore, 460 & 450 are not in Col 5.

7. If 460 & 450 are in Col 3, then columns 2 & 4 must both sum to 900 by Clue 6. It is impossible to do this with the scores remaining. Therefore, 460 & 450 are in Col 2 or Col 4, both of which must sum to 910, and Col 3 must sum to 920.

8. By Clue 5, Dolly's score is 410, 420, 430, or 440, while Jerry's score is 420, 430, 440, or 450 respectively, and Frank's score is 470, 480, 490, or 500 respectively. If Dolly is 420 or 430, then Jerry is 430 or 440 respectively and both are in Row 2. But there is not room in Row 2 for Dolly and Jerry with these scores, so Dolly is neither 420 nor 430.
   If Dolly is 440, then she is in Seat 9, and Jerry is 450 and must be in Seat 2 by arguments 7 & 2. Then Hugh is 460 by argument 3. But then Seat 4 must be 470 in order to have the same average score for columns 2 & 4 (Clue 6). This contradicts 470 being the score for Seat 1, so Dolly is not 440. Therefore, Dolly is 410 in Seat 6, Jerry is 420 in Seat 9, and Frank is 470 in Seat 1.

9. From argument 7, Seat 7 must be 460 and Seat 2 must be 450. Since Col 4 sums to 910, Seat 4 must be 490. Col 3 sums to 920, so Seat 8 is 440 and Seat 3 is 480. This leaves 430 for Seat 10 and 500 for Seat 5. The seating chart now looks as follows:

   		Column 1	Column 2	Column 3	Column 4	Column 5
   ROW 2	Name	6. Dolly	7. Hugh	8. Ida	9. Jerry	10. George
   	Score	410	460	440	420	430
   ROW 1	Name	1. Frank	2.	3.	4.	5.
   	Score	470	450	480	490	500

10. By Clue 3, Eve must be in Seat 2, Ann in Seat 3, Chuck in Seat 4, and Bill in Seat 5.

Answer.

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