Dice Game

 

 

Sorting Numbers

 

 

1. Arrange the digits 1-9 in a line so that each pair of adjacent digits differs by either 2 or 3.
2. Arrange the digits 1-9 in a line so that each pair of adjacent digits sums to a prime number.
3. Now arrange the digits 1-9 in a line so that each pair of adjacent digits (when read as a two-digit number) appears in the times tables from 1 × 1 up to 9 × 9.

 

 

 

        Source: Katie Steckles, The New Scientist

Dart Puzzle

 

 

 

3

Three Dogs

 

Source: Puzzle Move

Palindromic times

 

 

 

 

 

 

 

 

1. A time such as 3:59:53 is palindromic, that is, it reads the same forward and backward. in a day starting from 0:00:00 to 23:59:59, there are 660 occasions when the time is palindromic. Among them which of the two is closest?

    

    

   Source: Nobuyuki Yoshigahara
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

09:59:59 and 10:00:01

Lucky Seven

 

 

 [Resource]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(95/247)+(86/13)

 

 

 

 

 

 

Cutting Puzzle

 This lovely puzzle is from professor Tanya Khovanova's blog.

You are given a 5-by-7 rectangle with two corners cut out: A 1-by-1 tile is cut from the bottom left corner, and a 1-by-2 tile is cut out of the top right corner, as in the picture. The task is to cut the resulting shape into two congruent polyominoes.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cryptarithm: Thirty

  

Answer: 810386

Cryptarithm: Joking

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer: 571428

Cryptarithm

 

391+803+803+84611+84611=171219

Cryptarithm: "NO GUN NO HUNT"

 

 

87+908+87=1082

Full part of the glass

 source: Presh Talwalkar

What comes next?

  

How many watermelons?

 

Can you solve it in 5 seconds?

Plant Puzzle

 

from SKG

Some solutions

System of Equations Puzzle

from: Matematik Dünyası

 

Runner's Puzzle

The source of this problem is

Puzzle a Day

@PuzzleADayBlog

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Two Numbers

Tax Collector Game

photo by Kelly Sikkema

Source of this activity:By Gary Antonick, New York Times

Tax Collector is played like this: Start with a collection of paychecks, from $1 to $12. You can choose any paycheck to keep. Once you choose, the tax collector gets all paychecks remaining that are factors of the number you chose. The tax collector must receive payment after every move. If you have no moves that give the tax collector a paycheck, then the game is over and the tax collector gets all the remaining paychecks. 

The goal is to beat the tax collector.

Example:
Turn 1: Take $8. The tax collector gets $1, $2 and $4.
Turn 2: Take $12. The tax collector gets $3 and $6 (the other factors have already been taken).

Turn 3: Take $10. The tax collector gets $5.

You have no more legal moves, so the game is over, and the tax collector gets $7, $9 and $11, the remaining paychecks. 

Total Scores:
You: $8 + $12 + $10 = $30.
Tax Collector: $1 + $2 + $3 + $4 + $5 + $6 + $7 + $9 + $11 = $48. 

Questions:

Is it possible to beat the tax collector in this $12 game? If so, how? What is the maximum score you can get?

Bonus: What if you played the game with paychecks from $1 to $24? How about $1 to $48?

 

Lockers and Bulbs

Task 1 (Source: Illustrative Math)

The 20 students in Mr. Wolf's 4th grade class are playing a game in a hallway that is lined with 20 lockers in a row.

• The first student starts with the first locker and goes down the hallway and opens all the lockers.
• The second student starts with the second locker and goes down the hallway and shuts every other locker.
• The third student stops at every third locker and opens the locker if it is closed or closes the locker if it is open.
• The fourth student stops at every fourth locker and opens the locker if it is closed or closes the locker if it is open.

This process continues until all 20 students in the class have passed through the hallway.

1. Which lockers are still open at the end of the game? Explain your reasoning.
2. Which lockers were touched by only two students? Explain your reasoning.
3. Which lockers were touched by only three students? Explain your reasoning.
4. Which lockers were touched the most?