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## Guess That Number I

Math brain teasers require computations to solve.

 Puzzle ID: #37011 Fun: (2.71) Difficulty: (1.35) Category: Math Submitted By: pokpic

"And welcome back to Guess That Number! Before the break Mr. Pok got to the 1 million dollar question! So, Mr. Pok how are you feeling?"
"Very nervous Bill, very nervous," replied Mr. Pok.
"Okay Mr. Pok, you know what to do. We'll put a set of clues on are screen, and you must figure out what number we're talking about! Today, the mystery number is represented by A. Mr. Pok, if you can figure out what number A stands for in 2 minutes or less, we'll give you 1 million dollars! Are you ready?" asked Bill.
"I hope so," answered Mr. Pok.
"Okay! The clues are on our screen! On your mark! Get set! GO!" screamed Bill.
Mr. Pok turned around and faced the screen. My challenge to you is can you help Mr. Pok win the million dollar prize? Here are the clues given to Mr. Pok:
1. 100 is larger than A.
2. A is larger than 30.
3. A is a multiple of 6.
4. The sum of A's digits is 9.
5. The number in the tens place is larger than the number in the ones place.
6. The difference between A's digits is 1.
Mr. Pok figured out the answer and scribbled it down on the notebook in front of him right when the buzzer sounded. He raised his answer for all to see.
"Congratulations Mr. Pok! You have won 1 million dollars!" Bill said into the microphone.
What number did Mr. Pok write in the notebook?

Mr. Pok wrote 54.

We first start with clue number 1. We figure out A is less than 100. Next we look at clue number 2. We figure out that A is bigger than 30. So we now know that A has to be between 31 and 99.

The third clue tells us that it has to be a multiple of 6. So you write down all the multiples of six between 31 and 99. The multiples are 36, 42, 48 54, 60, 66, 72, 78, 84, 90, and 96.

Next, we find out that the sum of A's digits is 9, so we can cross out 42, 48, 60, 66, 78, 84, and 96. Next, we find out that the number in the tens place is larger than the number in the ones place so we can cross out 36. The last clue tells us that the difference between A's digits is 1. So therefore the only number that fits all 6 clues is 54.

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