## Scratch My Head

Tear one off and scratch my head,

What once was red is black instead.

What is it?

**SOLUTION**

The answer is MATCHSTICK.

Tear one off and scratch my head,

What once was red is black instead.

What is it?

The answer is MATCHSTICK.

How many numbers between 1 and 100 can you pick at most, so that none of them divides another?

You can choose at most 50 numbers: 51, 52, 53, …, 100.

In order to see that you cannot choose more than 50, express each number in the form **2ⁿ×m**, where **m** is an odd number. Since no 2 numbers can have the same **m** in their expressions, and there are only 50 odd numbers between 1 and 100, the statement of the problem follows.

I am big on Saturday and Sunday.

I am small on Tuesday, Wednesday, and Thursday.

I am not on Monday and Friday.

What am I?

The answer is the letter S.

White to play and mate Black in 20 moves.

The moves are as follows:

- Qb7+ Rc5c6
- Qa5+ Rc4c5
- Qb3+ Rd4c4
- Qd2+ Re4d4
- Qf3+ Re5e4
- Qg5+ e5
- Qf7+ Rd6e6
- Qd8+ Rc6d6
- Qb7+ Rc5c6
- Qa5+ Rc4c5
- Qb3+ Rd4c4
- Qd2+ Re4d4
- Qf3+ e4
- Qg5+ Re6e5
- Qf7+ Rd6e6
- Qd8+ Rc6d6
- Qb7+ Rc5c6
- Qa5+ Rc4c5
- Qb3+ Rd4c4
- Qd2x

In each set of 6 pictures, find the 2 matching ones.

The matching pairs are:

- ZEBRAS: #1 and #4
- ELEPHANTS: #2 and #6
- GIRAFFES: #3 and #4
- HYENAS: #1 and #4
- VULTURES: #2 and #3

One night, a man received a call from the Police. The Police told the man that his wife was murdered, and that he should get to the crime scene as soon as possible. The man immediately hung up the phone and drove his car for 20 minutes. As soon as he got to the crime scene, the Police arrested him, and he got convicted for murder.

How did the Police know that the man committed the crime?

The police did not tell the man where the crime scene was.

What does the liar do when he dies?

He lies still.

**Brain Drop** is a new puzzle podcast by Brian Hobbs, released on a (mostly) weekly basis. In each episode, Brian presents 3 new puzzles and shares the solutions of the puzzles from the previous week. He uses professional voicework, music, and sound effects, to set up the mood and make his show more entertaining. Click the banner below to check out Brain Drop and see if you can answer Brian’s latest set of puzzles!

Find all 10-digit numbers with the following property:

- the first digit shows the number of 0s in the number
- the second digit shows the number of 1s in the number
- the third digit shows the number of 2s in the number, and so on

Let the number be **ABCDEFGHIJ**. The number of all digits is 10:

A + B + C + D + E + F + G + H + I + J = 10

Therefore, the sum of all digits is 10. Then:

0×A + 1×B + 2×C + 3×D + 4×E + 5×F + 6×G + 7×H + 8×I + 9×J = 10

We see that F, G, H, I, J < 2. If H = 1, I = 1, or J = 1, then the number contains at least 7 identical digits, clearly 0s. We find A > 6 and E = F = G = 0. It is easy to see that this does not lead to solutions, and then H = I = J = 0.

If G = 1, we get E = F = 0. There is a 6 in the number, so it must be A. We get 6BCD001000, and easily find the solution **6210001000**.

If G = 0, F can be 0 or 1. If F = 1, then there must be a 5 in the number, so it must be A. We get 5BCDE10000. We don’t find any solutions.

If F = 0, then the number has at least five 0s, and therefore A > 4. However, since F = G = H = I = J = 0, the number does not have any digits larger than 4, and we get a contradiction.

Thus, the only solution is **6210001000**.

Please confirm you want to block this member.

You will no longer be able to:

- See blocked member's posts
- Mention this member in posts
- Invite this member to groups
- Message this member
- Add this member as a connection

**Please note: **
This action will also remove this member from your connections and send a report to the site admin.
Please allow a few minutes for this process to complete.

You have already reported this