Enigma 984: Answers on the back
15 November 2019
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From New Scientist #2139, 20th June 1998 [link]
I have 8 cards and each card has a whole number on the back. Not all the 8 numbers are the same. On the front of each card there is a true statement about the number on the back of the car. The eight statements are as follows:
“The number on the reverse of this card is…
… 2 plus the number of cards with an even number on them;
… the total of the 8 numbers, divided by 5;
… the number of cards with a prime on them;
… the number of cards with a number larger than 3 on them;
… the difference between the largest number on the cards and the second largest number on the cards;
… the difference between the smallest number on the cards and the second smallest number on the cards;
… the number of cards that have the largest number on them;
… the difference between the number of cards that have the smallest number on them and the number of cards that have the second smallest number on them.”
When a statement refers to a number on a card it means the number on the back of the card. And an extra clue, which you do not actually need, is that if card A has a higher number on it than card B then card A comes before card B in the above list of statements.
What are the 8 numbers on the cards? Give them in descending order.