How many grains of sand do you need until you have a heap of sand?

[Ref: ZMQO]

Hint: Is a million grains of sand a heap?

Answer: We can safely say two things:

1. A million grains of sand is a heap.
2. If we remove one grain of sand from a heap, we still have a heap.

We can now keep repeating #2 until we only have a single grain of sand remaining. Is this a heap? Clearly not. But what went wrong with our thinking?

This is called the Sorites paradox (soros being Greek for "heap"), and is a classic paradox that has no real answer. Both #1 and #2 are true, and we can indeed keep removing one grain of sand until we have a single grain remaining. When does the heap become a non-heap? If we remove one more grain we're left with nothing, is this still a heap?

Puzzle 412

A farmer was asked how many chickens he had sold at market that day. His reply was:

I've had four customers today, and each bought half of my remaining chickens, plus a half chicken.

The farmer sold all of his chickens at market that day. How many chickens did the farmer sell?

Hint: How many chickens did the last customer buy?

Answer: 15 chickens.

The first customer bought 15 ÷ 2 + ½ = 8 (leaving 7)
The second customer bought 7 ÷ 2 + ½ = 4 (leaving 3)
The first customer bought 3 ÷ 2 + ½ = 2 (leaving 1)
The first customer bought 1 ÷ 2 + ½ = 1

The answer can be worked out in the following way:

The fourth customer can only have bought one chicken, otherwise there would be some chickens left. The third customer bought all but 1, so total - (total ÷ 2 + ½) = 1. This can be solved algebraically or it's easy to see that the total must have been 3. This method keeps working until we reach the first customer.

Puzzle 413

Name three consecutive days without using the words Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday.

[Ref: ZSNI]

Hint: What day is it today?

Answer: Yesterday, today, and tomorrow!

Note: Christmas Eve, Christmas Day and Boxing Day isn't correct as Boxing Day isn't always the day following Christmas Day.

Puzzle 414

I've been quite poorly lately and the doctor has prescribed me a two courses of tablets (Anvilite and Bigoxy) to solve my problem and I must take one of each at the same time, once every day.

These tablets are rather expensive so I've been very careful with them.

Last night I'd just got my Anvilite tablet. I was about to get my Bigoxy tablet when two tablets fell out of the bottle into my hand and joined the Anvilite tablet. This was a major problem for me as all three tablets were identical, the same size, the same weight, and neither had any markings on it. I had to take one of each but I couldn't tell them apart, and they were far too expensive to throw these three tablets away and start again.

What did I do?

[Ref: ZFSG]

Hint: Can I add something to the three tablets to help?

Answer:
I cut each of the three tablets in half, and created two piles (i.e. as I broke each tablet, I placed one half in the left pile and the other half in the right pile).

Each pile now had one half of Anvilite, and two halves of Bigoxy.

All I had to do was to split another Anvilite tablet, and place half in each pile, so each pile then had two halves of each tablet (i.e. a whole tablet), which is exactly how many I had to take.

I had one pile last night, and the other pile is for tonight.

Puzzle 415

Using the BrainTracker grid below, how many words can you find? Each word must contain the central K and no letter can be used twice, however, the letters do not have to be connected. Proper nouns are not allowed, however, plurals are. Can you find the nine letter word?