### Brain Teasers

# Dogs and Fleas

There are two dogs. Both have fleas.

If one flea jumps from the 1st dog to the 2nd, then both will have

the same amount.

Or if one flea jumps from the 2nd dog to the 1st, then the 1st will

have 5 times the amount of the 2nd.

How many fleas do each dog have before any jumping takes place?

If one flea jumps from the 1st dog to the 2nd, then both will have

the same amount.

Or if one flea jumps from the 2nd dog to the 1st, then the 1st will

have 5 times the amount of the 2nd.

How many fleas do each dog have before any jumping takes place?

### Answer

1st dog as 4 fleas2nd dog as 2 fleas

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## Comments

a=fleas on 1st dog, b=fleas on second.

Equations are:

a-1=b+1

5(b-1)=a+1

substitue and solve, or you can use intuition (you know numbers are low, leaving 1,2,3,4 as options - just imagine each combo and 2,4 emerge). Simple, but still good.

Equations are:

a-1=b+1

5(b-1)=a+1

substitue and solve, or you can use intuition (you know numbers are low, leaving 1,2,3,4 as options - just imagine each combo and 2,4 emerge). Simple, but still good.

OMG! I'm aweful at math! lol

If, after the first jump, they are equal then take it back and one goes up, one goes down. Therefore they must differ by 2. Now if the jump goes the other way they will differ by 4. What 2 numbers differ by 4 and the larger is 5 times the smaller? 5 and 1. So before the second jump they had 4 and 2 fleas respectively.

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