Saturday, March 22, 2014
Monday, March 17, 2014
Saturday, March 15, 2014
Monday, February 17, 2014
Dante's Infernal Puzzle Collection -- 20. Ardesiae
One way to approach this question is to think about how many of each digit you would need. Let's start with 0 and move up.
0: We need two 0-slates to make numbers like 500 or 600. The worst case scenario is that the four numbers we get are 100, 200, 300, and 400, or any combination with eight 0s altogether. Thus, we need eight 0s.
1: Suppose one of our choices is 111. The other three choices cannot be 111, but they can all include two 1s. So the number of 1s we need is 3 + 2 + 2 + 2 = 9.
2: Similarly, we need nine of these.
3: Again, nine
4: Again, nine.
5: Nine!
6: Nine!
7: Nine!
8: First, note that we never have to make 888. So we don't need to consider the worst case scenario that we considered for 1. However, we can still have a situation where all four numbers contain two 8s, in which case the number of 8s we need is 2 * 4 = 8.
9: This is the tricky part. Remember that the guy said we can make a 9 with a 6. The worst case scenario involving 9s and 6s would be when all four numbers have three digits and the digits only include 9 and 6: for example, {666, 669, 696, 699}. In this case, we need 4 * 3 = 12 of either 6 or 9. Note that we already have nine 6s. So we only need 3 more.
Add them up. We need eight 0s and eight 8s. We need nine of each of 1, 2, 3, 4, 5, 6, and 7. Finally, we need three 9s.
8 * 2 + 9 * 7 + 3 = 16 + 63 + 3 = 82.
Answer: 82
0: We need two 0-slates to make numbers like 500 or 600. The worst case scenario is that the four numbers we get are 100, 200, 300, and 400, or any combination with eight 0s altogether. Thus, we need eight 0s.
1: Suppose one of our choices is 111. The other three choices cannot be 111, but they can all include two 1s. So the number of 1s we need is 3 + 2 + 2 + 2 = 9.
2: Similarly, we need nine of these.
3: Again, nine
4: Again, nine.
5: Nine!
6: Nine!
7: Nine!
8: First, note that we never have to make 888. So we don't need to consider the worst case scenario that we considered for 1. However, we can still have a situation where all four numbers contain two 8s, in which case the number of 8s we need is 2 * 4 = 8.
9: This is the tricky part. Remember that the guy said we can make a 9 with a 6. The worst case scenario involving 9s and 6s would be when all four numbers have three digits and the digits only include 9 and 6: for example, {666, 669, 696, 699}. In this case, we need 4 * 3 = 12 of either 6 or 9. Note that we already have nine 6s. So we only need 3 more.
Add them up. We need eight 0s and eight 8s. We need nine of each of 1, 2, 3, 4, 5, 6, and 7. Finally, we need three 9s.
8 * 2 + 9 * 7 + 3 = 16 + 63 + 3 = 82.
Answer: 82
Sunday, February 16, 2014
Dante's Infernal Puzzle Collection -- 19. Grana
Suppose he sold x of units of the poor grains and y units of the fair grains.
His cost was 32x + 40y.
He sold x + y units of grains at the price of 43, so his revenue was 43x + 43y.
(32x + 40y) * (1.25) = 43x + 43y
40x + 50y = 43x + 43y
3x = 7y
x = (7/3)y
Suppose x + y = 100.
(7/3)y + y = 10/3y = 100
y = 30
x = 100 - 30 = 70
Thus, 70% of the grains he sold were poor, and 30% were fair.
Answer: 70% poor, 30% fair
His cost was 32x + 40y.
He sold x + y units of grains at the price of 43, so his revenue was 43x + 43y.
(32x + 40y) * (1.25) = 43x + 43y
40x + 50y = 43x + 43y
3x = 7y
x = (7/3)y
Suppose x + y = 100.
(7/3)y + y = 10/3y = 100
y = 30
x = 100 - 30 = 70
Thus, 70% of the grains he sold were poor, and 30% were fair.
Answer: 70% poor, 30% fair
Dante's Infernal Puzzle Collection -- 18. Domanda
The goal is to find out which gesture means yes and which means no. Ask a question whose answer must be yes -- for example, "Is this Hell?"
Subscribe to:
Posts (Atom)