Year 3 to Year 6: What Do You Need?
Can you sort out the four clues that help and the four clues that do not help in finding the number I am thinking of?
Four of the clues below are true but do nothing to help in finding the number.
Four of the clues are necessary for finding it.
Here are eight clues to use:
- The number is greater than 9.
- The number is not a multiple of 10.
- The number is a multiple of 7.
- The number is odd.
- The number is not a multiple of 11.
- The number is less than 200.
- Its ones digit is larger than its tens digit.
- Its tens digit is odd.
What is the number?
The answer is 35
- * statement 1 does not help because by following the other clues you can tell that you need more than 1 digit to find the answer and the only multiple of 7 smaller than 9 is 7, which consists of only 1 digit.
- * statement 2 does not help because the ones digit has to be larger than the tens digit and the only multiple of 7 and 10 is 70 and the 0 is smaller than the 7
- * statement 3 helps because being a multiple of 7 cancels out a lot of numbers that could have been possibilities.
- * statement 4 helps because by being an odd number it too cancels out a lot of other possibilities
- * statement 5 does not help because the only multiple of 7 and 11 is 77 and the ones digit has to be bigger than the tens digit and the two digits in 77 are even (even - meaning the same, I think) .
- * statement 6 does not help because you can only choose the numbers from 1-100, and those numbers are all below 200 anyway, so that statement is completely worthless.
- * statement 7 helps because by using it there will only be a few numbers left to choose from.
- * statement 8 helps because by using it you can easily narrow the number down so that there is only one left.
The only number left after using all of the useful clues is 35
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