Math Problems

You will need two six-sided dice to play this game.  Roll both dice and create a two digit number by taking the larger number followed by the smaller number.  If the numbers are the same, then the two digit number is going to be either 11, 22, 33, 44, 55, or 66 depending on what you rolled.  You win if you get a two digit number less than 50.  Play the game 100 times to determine your experimental probability of winning.  

You have a 7 minute and a 4 minute hourglass timer.  How would you use these to measure 9 minutes?  

Solution

Flip the 7 minute and 4 minute timer at the same time.  When the 4 is done, flip it again. When the 7 minute timer is done, flip it again.  When the 4 minute is done, flip the 7 minute timer.  When the 7 minute timer is done, 9 minutes will have passed from the first time the timers were flipped.  

In hockey, teams play three 20 minute periods.  At the end of a hockey game, Team A had 4 goals and Team B had 2 goals.  How many different Team A to Team B scores were possible at the end of the first period?   

The possible scores were: 

0-0,

0-1, 

0-2, 

1-0, 

1-1, 

1-2, 

2-0, 

2-1, 

2-2, 

3-0, 

Pick a two digit number.  Calculate 91 x (your number) x 111.  

What do you notice?

Try it with other two digit numbers.  

Why does this always happen?  

Solution

91 x 111 =10101 so when you multiply a two digit number by 10101, you get the two digit number repeated three times.  

A string of consecutive whole numbers that adds to 2024 is 179+180+181+182+183+184+185+186+187+188+189. 

Can you find another string of whole numbers that adds up to 2024?