“Club Math” is the first ever student math club at Kaua‘i Community College. The club is interested in the practicality and usefulness of mathematics in everyday living. The goal is to involve the community by promoting this ideal. What follows
“Club Math” is the first ever student math club at Kaua‘i Community College. The club is interested in the practicality and usefulness of mathematics in everyday living. The goal is to involve the community by promoting this ideal. What follows is the last math puzzle printed two weeks ago followed by the answer. The club submits weekly brainteasers for the education page.
What number am I?
I am a three digit number.
My tens digit is five more than my ones digit.
My hundreds digit is eight less than my tens digit.
What number am I?
Solution:
It’s not as confusing as it may sound; take it digit-by-digit. The key is to work backwards. From the hundreds digit, we know that one is the only number that can work (since we have to add eight to get the tens digit), because anything larger will make a number too big, and anything smaller would make a number too small. Since we know to add eight to one, we can get our second digit, which is nine. Lastly, we now have to subtract five to get the ones digit (9 – 5 = 4). When we put our solution together, we get 194.
We can also set up an inequality to help visualize the solution.
We know that all numbers have to be single digits greater than zero.
Hundreds digit: (X):
0 < X + 8 < 10 – 8 < X < 2 X = 1
Tens Digit: (Y):
X + 8 = Y, (1) + 8 = 9
Ones digit: (Z):
Y = 5 + Z, Y – 5 = Z,
(9) – 5 = Z, Z = 4
This week’s
brain teaser
The missing dollar:
Three friends check into a motel for the night and the clerk tells them the bill is $30, payable in advance. So, they each pay the clerk $10 and go to their room. A few minutes later, the clerk realizes he has made an error and overcharged the trio by $5. He asks the bellhop to return $5 to the three friends who had just checked in. The bellhop sees this as an opportunity to make $2 as he reasons that the three friends would have a tough time dividing $5 evenly among them; so, he decides to tell them that the clerk made a mistake of only $3, giving a dollar back to each of the friends. He pockets the leftover $2 and goes home for the day. Now, each of the three friends gets a dollar back, thus they each paid $9 for the room which is a total of $27 for the night. We know that the bellhop pocketed $2 and adding to the $27, you get $29, not $30 which was originally spent. Where did the other dollar go?
