### Brain Teasers

# Three Statements IV

Which of these three statements are true?

1. Sam received $0.41 change from a purchase. If he received 6 coins, 3 of the coins had to be dimes.

Coins in circulation are: 1 cent, 5 cents, 10 cents, 25 cents. 1 dime=10 cents.

2. If there are more inhabitants in Los Angeles than there are hairs on the head of any inhabitant, and if no inhabitant is totally bald, it necessarily follows that there must be at least two inhabitants with exactly the same number of hairs.

3. The price of a T-shirt was cut 20% for a sale. The price of the T-shirt should be increased by 25% if it is to be sold again at the original price.

1. Sam received $0.41 change from a purchase. If he received 6 coins, 3 of the coins had to be dimes.

Coins in circulation are: 1 cent, 5 cents, 10 cents, 25 cents. 1 dime=10 cents.

2. If there are more inhabitants in Los Angeles than there are hairs on the head of any inhabitant, and if no inhabitant is totally bald, it necessarily follows that there must be at least two inhabitants with exactly the same number of hairs.

3. The price of a T-shirt was cut 20% for a sale. The price of the T-shirt should be increased by 25% if it is to be sold again at the original price.

### Answer

All the three statements are true.In statement 1, there must be one 1 cent because of the remainder upon division by 5. The remaining 5 coins total 40 cents, which can only be 5*2+10*3.

In statement 2, the pigeonhole principle is used, and you should know it.

In statement 3, if the original price is X, then X*(1-0.2)*(1+0.25)=X*0.8*1.25=X, which is again the original price.

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