### Brain Teasers

# How Many Candies?

Rob the robot went to the candy-store to buy some candies. He found his favorite gums in front of him, in packages of 225 gums in each.

Though extremely intelligent, he is still a robot, thus capable of using only 1's and 0's.

What is the minimum number of gums that Rob ate that day if he finished all of his packages, and the number of gums contained nothing but 1's and 0's?

Oh yes, and you can't cheat and use binary notation. The answer is in base 10, but still only uses 1's and 0's.

Though extremely intelligent, he is still a robot, thus capable of using only 1's and 0's.

What is the minimum number of gums that Rob ate that day if he finished all of his packages, and the number of gums contained nothing but 1's and 0's?

Oh yes, and you can't cheat and use binary notation. The answer is in base 10, but still only uses 1's and 0's.

### Hint

Think of the factors of 225, and kids, don't try this at home (or you would suffer from a severe stomach ache).### Answer

11,111,111,100This contains nine ones, so it is divisible by 9, and two 0's at the end, so it is divisible by 25.

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## Comments

Good puzzle. Unfortunately your comment about binary bedazzled me and I somehow read 225 as 255 (11111111 in binary). No wonder I couldn't get it! Well done!

This is just too hard to be fun

@cccc Too hard to be fun???? I did not think it was all that hard, but then I enjoy sitting around trying to find the answer to math problems.

Very nicely done!

Instead of multiples of 225 try multiples of 900. (4 X 225) The answer must end in "00."

The answer should be easier to find as the product = 12345679 X 900.

The answer should be easier to find as the product = 12345679 X 900.

"This contains nine ones, so it is divisible by 9," Is this some truth about any number that contains nine ones? Or, a tangled way of saying its digits add up to nine, so it is divisible 9? (225 obeys the second version.)

Interesting puzzle. Once I got to 99 + 9 = 108 I realized this would keep repeating and that I'd need to have all 1's until the final two zeros.

The explanation is cleaner, since the number can be easily determined by the simple fact that it must contain nine 1's and must end in two zeros.

By the way, the real answer based on the wording of the teaser is zero since there is no requirement that Robbie actually buys any packs.

The explanation is cleaner, since the number can be easily determined by the simple fact that it must contain nine 1's and must end in two zeros.

By the way, the real answer based on the wording of the teaser is zero since there is no requirement that Robbie actually buys any packs.

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