# math puzzles .. =) xD know em?

1) What is the missing number in the following sequence ? (explain why)

3 7 15 __ 63 127

2) If a teenager and a half can eat a pizza and a half in a day and a half, how many pizzas can a dozen

teenagers eat in three days?

3) You have 12 coins, one of which is counterfeit and weighs less than the legal coins. How can you use a

simple balance 3 times to determine which coin is counterfeit?

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1. Double and add 1 = 31

2. A teenager and a half can eat a pizza and a half in a day and a half, therefore

A teenager can eat a pizza in a DAY AND A HALF

A teenager can eat TWO pizzas in THREE days

12 teenagers can eat TWENTY FOUR pizzas in 3 days.

3. Weigh 6 on each side - discard the heavier 6

Of the lighter 6, weigh three on each side - discard the heavier three

Weigh one against another . If they balance, then the remaining one is the fake. If they donâ€™t balance then the lighter of the two is the fake.

Second alternative

1. Place 4 on each side of the balance.

If they balance then the fake is among the ones not yet put on the balance so discard all 8 on the balance. if they dont balance, the fake is in the lighter 4. Therefore discard the heavier 4 and also the 4 not yet placed on the balance. In either scenario the fake is one of 4.

2. Place 2 of the 4 on each side of the balance. Discard the heavier 2

3. Place one of the remaining 2 on each side of the balance. The lighter one is the fake.

double add 1

How can a "teenager and a half" eat a pizza? What half of the other teen? Bottom half canâ€™t eat at all, and top half canâ€™t digest.

put 6 coins on each side, discard coins that are heaviest.

put 3 coins on each side, discard coins that are heavies.

put one coin on each side, if both sides are same, remaining coin is fake. Or whatever coin is lighter from the two you weighed.

1) 31, because the amount that is added each time is doubled: to begin with, 4 was added, then 8, then 16 (to get 31), then 32 (to get 63)

2) (A teenager and a half!? Where you gettinâ€™ your teenagers at, boy? [...or girl?])

So that means that 1 teenager can eat 1 pizza per day, so 12 teenagers can eat 12 pizzas in 1 day.

In 3 days: 12 x 3 = 36 pizzas

3) Put 6 coins on either side of the balance, then take the pile of 6 that weighs the least.

Split this pile into two piles of 3 coins.

Now put these two piles on either side of the balance, and again take the pile that weighs the least.

Now, you have 3 possible coins that are the counterfeit one. Choose two of them at random, and put 1 on either side of the balance. If they weigh the same, the one not chosen is the counterfeit one, else it is the lightest coin on the balance.

1) The amount being added is doubling each time 3 + 4 = 7, 7+8=15, 15+16 = 31, 31+32=63. So the missing number is 31.

2) 12 teenagers * 1 pizza = 12 pizzas

12 pizzas * 3 days = 36 pizzas

3) First divide them in half and the pile that weighs less has the fake coin. Then divide that in half again. Then you are left with three coins and weigh two of the coins if they weigh the same then the one not being weighed is the counterfeit and if the one of the ones being weighed weighs less than it is the counterfeit.

1. 31

2. 24?

3. I donâ€™t know