Bagels Puzzle 1 Answer printable pdf download

Bagels Puzzle 1 Answer

Solution to Bagels Puzzle 1

What do you know after the first three guesses

in Game 1?

Answer: You know that exactly one of the three digits (6, 7

or 4) is correct but in the wrong place, exactly one of the

three digits (0,3 or 2) is correct but in the wrong place, and

exactly one of the three digits (5, 1 or 9) is correct and in

the right place. Since all three digits are from these

numbers, you now know that the only digit not tested, 8, is

not in the answer.

2. What do you know after guess #4?

Answer: You know that in addition to 8, the digits 3, 4, and

9 are also not in our solution (because of bagels in

response to guess 4).

3. What do you know after guess #5?

Answer: Since 560 gives you a pico (Guess 5), and 519

gives you a fermi (Guess 3), then 5 is out because 5

cannot be correct in the first position and also incorrect in

the first position. Since both 5 and 9 are eliminated this

means that 1 must be correct and is in the middle position

(fermi in response to guess 3). Thus we know: __ 1 __.

Likewise we know that 0 is eliminated because if 0 is one

of the digits it cannot be in the first position (see guess #2)

and it cannot be in the last position (see guess #5), then

since 1 is in the middle position we know that 0 cannot be

in the middle position. Therefore, if 5 and 0 are eliminated

then 6 must be one of the digits (see guess #5). If 6 cannot

be in the first or second position then 6 must be in the third

position. We now know __16.

4. What is the 3-digit number? Explain.

Answer: So far we have eliminated 0, 3, 4, 5, 8, and 9. If 0

and 3 are eliminated then 2 must be our third digit (see

guess #2). Thus our 3-digit number is 216.

Bagels Puzzle 1 Answer