Brain Teasers
Twos and Fives
We have 10 2's and 10 5's. Pick some of them, and add them together. If we pick them all, we get the sum 70. Which sums between 1 and 70 are impossible?
Hint
1 and 3 are impossible.Answer
By symmetry, 67 and 69 are also impossible. Other sums can be constructed easily.Therefore, four sums 1, 3, 67 and 69 are impossible.
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Can anyone tell me if there is a way of actually knowing the answer without trial and error
woh that one was hard and i didnt get it lol but great teaser!!!
Too easy but good anyway
Symmetry, as fairelamour uses the word, means to reach an amount one must leave the complementing amount in the stack, to have $2 in hand you will leave $68 in the stack, and vice versa. It is process of elimination, which is considerably faster than trial and error, that tells us $2 notes and pairs of $5 notes can account for all the even numbers from 0 to 70. ( {0,2,4,6,8,10} + {0,10,20,30,40,50,60} where {...} means pick one) Eliminate the the amounts reached with odd numbers of $5 notes. ( {0,2,4,6,8,10} + {5,15,25,35,45,55} ) It should be apparent this is every odd amount from 5 to 65. And, the answer is as stated the odd amounts below 5 and above 65.
Somehow, I got it right away after I read it 3 times.
Pretty easy but a fun teaser!
Interesting to solve, not very difficult!
Interesting to solve, not very difficult!
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