When is the math test?

Logic Level 2

Five girls are not in complete agreement about the date of the Math test.

  • Andrea says it will be in August, 16th, Monday;
  • Daniela says it will be in August, 16th, Tuesday;
  • Fernanda says it will be in September, 17th, Tuesday;
  • Patricia says it will be in August, 17th, Monday;
  • Tatiane says it will be in September, 17th, Monday.

Only one of them is completely right.
The others guessed at least one of these information correctly: the month, the day or the weekday.
Who is right?

Problem Source: OBMEP 2014

Image credit: Wikipedia Peter van der Sluijs
Patricia Daniela Tatiane Fernanda Andrea

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4 solutions

Discussions for this problem are now closed

Danny Whittaker
Dec 5, 2014

Fernanda and Andrea completely contradict each other. Likewise for Tatiane and Daniela. Thus Patricia.

Jose Tumulak
Dec 12, 2014

Since it said that only one of the 5 girls was completely right and that the others guessed at least one of these information correctly: the month, the day, or the weekday, my solution was simple deduction really, I first scanned the answers these girls came up with starting from which answer was given first, i came up with August 3x September 2x, then i went to the day of the month part which was 16th 2x and 17th 3x, then the weekday which was Monday 3x and Tuesday 2x after that I went with the highest of each answer that was given and ended up with - - - August 17 Monday which was also Patricia's answer

For those who may have gotten confused on what x means in my solution it means times, i was just too lazy to write the actual 5 letter word that many times so ya, laziness

Kit Gallagher
Dec 11, 2014

The key bit is that everyone has something right.

So assume it is in September. In that case it must be on the 17th (the only option.) As Andrea and Daniela have both then got the month and date wrong, they must get the day right, yet they cannot, as they are not guessing the same day. Therefore it cannot be in september.

If it is August, then Fernanda and Tatiane have got the month wrong. As they cannot both get the day right (for they are guessing different days) the only thing they can both get right is the date. Therefore it must be the 17th.

As it is not September (therefore it is august) and it is the 17th, the person who is right is Patricia.

Marcus Jeffries
Dec 11, 2014

If aug16 is a mon/tues, sept 17 will not be either mon or tues. Thus all 4 of these possibilities are incorrect, leaving Patricia as the correct option.

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