In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science, and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and others missed two examinations. Nobody missed more than two examinations.
The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations.
If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for.
If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for.
The marks obtained by six students in the examinations are given in the table below. Each of them missed either one or two examinations.
| |
English |
Hindi |
Mathematics |
Science |
Social Science |
| Alva |
$80$ |
$75$ |
$70$ |
$75$ |
$60$ |
| Bithi |
$90$ |
$80$ |
$55$ |
$85$ |
$85$ |
| Carl |
$75$ |
$80$ |
$90$ |
$100$ |
$90$ |
| Deep |
$70$ |
$90$ |
$100$ |
$90$ |
$80$ |
| Esha |
$80$ |
$85$ |
$95$ |
$60$ |
$55$ |
| Foni |
$83$ |
$72$ |
$78$ |
$88$ |
$83$ |
The following facts are also known.
- Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations.
- The student who missed Mathematics examination did not miss any other examination.
- One of the students who missed the Hindi examination did not miss any other examination. The other student who missed the Hindi examination also missed the Science examination.
For how many students can we be definite about which examinations they missed?