A Twist To It Quiz Puzzle Answer

You have a pack of nine cards numbered from one to nine.

You can split the cards into groups in many ways. For example, you could have 1, 2, 5 and 7 in one group, and 3, 4, 6, 8 and 9 in a second group. In this case the first group (1, 2, 5 and 7) adds up to 15 and the second group (3, 4, 6, 8 and 9) adds up to 30. So the second group totals twice the first group.

Now your challenge is to put the cards in two groups, one of four cards and the other five cards, so that one group totals three times the other group.

It may seem impossible, but there is a twist to it.

The reason it seems impossible is that for one group to total three times the other group the sum of all the cards must be a multiple of four. And 45 is not a multiple of four. [It is a multiple of three, which makes the example grouping possible.]

But we have said there is a twist to it, and the twist is to turn the card with a six on it upside down, making a second nine. Now the total of all the cards is 48, and this is a multiple of four.

The groups are then 1, 2, 4 and 5 (which totals 12) and 3, 7, 8, 9 and 9 (which totals 36)


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