### Brain Teasers

# The Number Lier

There are 3 numbers 0-9.

Eric knows the product and says, "I know the numbers."

Then, everyone is told that one digit is exactly one greater than another.

Then, Luke is told one of the numbers and says, "Eric lied."

Then you are told the numbers add up to 11.

What are the numbers?

Eric knows the product and says, "I know the numbers."

Then, everyone is told that one digit is exactly one greater than another.

Then, Luke is told one of the numbers and says, "Eric lied."

Then you are told the numbers add up to 11.

What are the numbers?

### Answer

0, 5, 6Eric knows the product and claimed that he knows the numbers.

Luke is told a number and then he knows Eric lied.

If Luke had received an 8, the combination could be 8,8,8, which is the only combination that multiplies to 512; Luke wouldn't know Eric lied.

If Luke received 6, the combination could be 6,7,7 which is the only combination that multiplies to 294, so Luke wouldn't know Eric lied.

If Luke received 2 or 7; 2x7x7=98.

4 or 5; 4x5x5=100.

3 or 9; 3x9x9=243.

1; 1x1x1=1.

Luke would only know that Eric lied if Luke was given a 0.

Therefore one of the digits is 0.

The remaining two digits must add to 11 because 11-0=11.

Two of the digits are one apart so that leaves:

0 & 1 + 10

5 & 6 + 0

However, 10 isn't an option so it must be 0, 5, 6.

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