Five children sat a scholarship exam and were tested in three subjects: Science, English, Mathematics, Geography and History. There were ten marks available in each subject, split between the candidates.
The order of the candidates after the tests was; 1) Pamela, 2) Will, 3) Fiona, 4) Chrissie and 5) Dan.
Each child was top in one subject.
In every subject no candidates got the same marks as each other.
Dan was top in History and Will top in Geography.
Fiona was top in Science, got the same marks in English as in Mathematics, and got the same marks in Geography as in History.
Chrissie was top English and third in Mathematics.
In Science Dan was second and Pamela third.
Will did not come last in any of the five subjects, and did better than Pamela in two subjects.
Dan received as many marks in one subject as he did in the other four put together.
As we are told that in every subject all five candidates received different marks, the five marks must be 0, 1, 2, 3 and 4.
So we can now fill in all the marks that we have been given. Note that we have the top candidate in four of the subjects and all the children were top in one subject, so we can infer the fifth.
We now know first, second and third in Science, and know that Will came last in no subjects, so he came fourth and Chrissie came last.
We know that Dan gained 4 marks in History and got as many marks in one subject as the other four put together. Therefore he got a total of 8 marks from the five subjects. As he was the bottom candidate we can infer that Chrissie got 9 marks, Fiona got 10 marks, Will got 11 marks and Pamela got 12 marks.
So we have:
| Science | English | Mathematics | Geography | History | Total | |
| Pamela | 2 | 4 | 6 | |||
| Will | 1 | 4 | 5 | |||
| Fiona | 4 | 4 | ||||
| Chrissie | 0 | 4 | 2 | 6 | ||
| Dan | 3 | 4 | 7 |
Dan has 7 marks and only got 8 in total, so his missing marks must be 0, 0 and 1.
Chrissie has 6 marks and got 9 in total, so her missing marks must be 0 and 3 or 1 and 2.
We know that Fiona got the same marks in English and Maths and the same marks in Geography and History, so her missing marks must be two 0s and two 3s or two 1s and two 2s.
Will's missing marks must be 1, 2 and 3.
Pamela's missing marks are 1, 2 and 3 or 0 and two 3s.
From this we can fill in the table as follows:
| Science | English | Mathematics | Geography | History | Total | |
| Pamela | 2 | 3 | 4 | 3 | 0 | 12 |
| Will | 1 | 2 | 3 | 4 | 1 | 11 |
| Fiona | 4 | 1 | 1 | 2 | 2 | 10 |
| Chrissie | 0 | 4 | 2 | 0 | 3 | 9 |
| Dan | 3 | 0 | 0 | 1 | 4 | 8 |