Oh. I see. That’s what you get when the rate varies linearly with the height (or radius, as that varies linearly with height). But it really burns at a constant volume, which isn’t the same thing.
I didn’t feel like playing along, but I did get the first word right away.
I was thinking clues could include haggis, scotch, and poet/poetry, and luckily haggis was first. I clicked your spoiler without looking for others.
A pile of 100 coins consists entirely of pennies, nickels, dimes, and quarters. It contains at least four of each. The value of the pile is $2.73. How many pennies are there?
83
2 Likes
I got 83 too
Summary
4 quarters = $1
5 dimes = $0.50
8 nickels = $0.40
83 pennies = $0.83
1 Like
I got 83 too
Same!
Summary
a little linear algebra, a little brute-force.
p + n + d + q = 100 (100 coins)
p + 5n + 10d + 25q = 273 (273 cents in total value)
…
4n + 9d + 24q = 173
p, n, d, q are integers >= 4
Assume q = 4.
then
4n + 9d = 77
since 4 is even, 4n will be even. Therefore 9d must be odd, so d must be odd as well.
if d=5, n = 8
if d=7, n = 3.5
if d=9, n = -1
Thus d = 5, otherwise could not satisfy all conditions.
Not done yet! q could be > 4.
If q = 5,
4n + 9d = 53
if n=4, d=4, 16 + 36 = 52 <> 53
if n=4, d=5, 16 + 45 = 59 <> 53
if n=5, d=4, 20 + 36 = 56 <> 53
any other solution will also not balance the equation, so q =/= 5.
Therefore:
q = 4
d = 5
n = 8
and 100 - 4 - 5 - 8 = 83 = p
2 Likes
I had to look back to see what the traditional response was:
Correct!
1 Like
Alf, Bert, Charlie, Duggie, and Ernie are placed in an order of merit (1st to 5th) with no ties. Charlie and Duggie are next to each other in the order and they each make two remarks. Those made by the one who was higher in merit are both false, those made by the other are both true.
CHARLIE: 1) Ernie’s place was half way between those of Bert and Charlie 2) Duggie was 3rd
DUGGIE: 1) Alf’s place was half way between those of Charlie and Ernie. 2) Bert was higher than Alf and Charlie.
What is the order of merit (from highest to lowest) with 1st being highest?
Alf, Bert, Charlie, Duggie and Ernie were arranged by merit in this order…
Summary
Bert, Ernie, Alf, Charlie, Duggie
Summary
If Charlie is telling the truth, Duggie is 3rd, meaning Charlie is either 4th or 2nd. But if Charlie is 4th or 2nd, there is no way that Ernie can be half way between Bert and Charlie. So Charlie is lying.
So we know Duggie is not 3rd and we know Ernie is not halfway between Bert and Charlie. We also know that Alf’s place was half way between Charlie and Ernie and Bert is higher than Alf and Charlie. We also know Charlie and Duggie are next to each other and Charlie is higher in merit.
Halfway between can only be 1-3-5 or three consecutive places.
If 1-3-5, it would have to be E, B, A, D, C otherwise, Bert couldn’t be higher than both Alf and Charlie. But this can’t be true because Duggie is ahead of Charlie.
So it must be 3 consecutive places. And it must be either 2-3-4 or 3-4-5, so that Bert can be ahead of Alf and Charlie.
If it was 3-4-5 it would have to have Charlie at 3, so Duggie can be next to him, but then Duggie would be higher than Charlie and that can’t be true.
So it must be 2-3-4. Bert must be at 1 to be ahead of the others, and Charlie must be at 4 to be next to Duggie.
Leaving us with Bert, Ernie, Alf, Charlie, Duggie
1 Like
Correct!