Below are two puzzles you might want to try asking your family and friends over the holidays. Try them out yourself, however, first.

Both questions are simple questions, and both look as though they have obvious answers. Both are questions that, if you think too quickly and go with your gut, you’ll probably get incorrect the first time. Then, if you take a step back, and actually think about them and do the math, you should be able to get the correct answer without too much trouble.

Neither of these questions are trick questions. Neither should leave a sour taste in the mouth when the answer is revealed. For both questions, I’ll reveal the answer in stages. After reading the question, give your first answer, then, click on the progressive buttons to reveal the correct answer, and finally the solution and explanation.

Question 1: Donut Sharing

Alice and Bob go into their local donut shop. Alice buys five donuts, and Bob buys three. As they are leaving, they meet Charlie and decide to cut-up, and share, all eight donuts equally between the three of them. After the feast, Charlie reaches into his pocket and discovers he has $0.80 in coins. Even though he knows that this amount of money is less than his share of the donuts eaten, he wants to compensate, as fairly as possible, Alice and Bob.

Question: How much of the money should he give Alice, and how much should he give Bob?

(All the donuts are same price, everyone eats the same amount, and ‘fair’ means repayment of Alice and Bob equal percentages of their own individual outlays).

Answer

When you think you have you answer, click the button on the right.

Did you suggest that Alice receives $0.50, and Bob $0.30? That’s not correct! Click the next button to reveal the correct answer.

It’s fairer for Alice to receive $0.70, and Bob to receive $0.10 Click the final button for a full explanation.

Explanation

We have to remember that everyone consumes donuts.

There are eight donuts, so each person consumes 8÷3 donuts (2^{2}/_{3} donuts).

This means that, in addition to her own consumed share, Alice donated 5 − 2^{2}/_{3} donuts to Charlie = 2^{1}/_{3} = ^{7}/_{3}.

Bob, on the other hand, after consuming his 2^{2}/_{3}, donated just ^{1}/_{3}.

As Alice donated ^{7}/_{3} donuts to Charlie and Bob ^{1}/_{3}, it’s only fair for Alice to receive $0.70, and Bob just $0.10

Question 2: 100m Race

After their donut feast, the three friends decide to exercise to burn off some calories. They challenge each other to 100m sprints.

Alice races againt Bob, and beats him by 20 meters (as Alice is crossing the finish line, Bob is 20 meters behind).

Bob races against Charlie, and beats him by 20 meters.

Question: If Alice raced against Charlie, how much would she beat him by?

(If we make the assumption that each person runs at a fixed, consistent, and constant speed on each and every race).

Answer

When you think you have you answer, click the button on the right.

Did you think that Alice would beat Charlie by 40m? That's not correct.

Alice will beat Charlie by 36m. Click the final button for a full explanation.

Explanation

We need to find their speeds.

When Alice has finished the 100m race, Bob is at 80m, so he runs at 80% of Alice's speed.

Similarly, Charlie runs at 80% of the speed of Bob.

Therefore, Charlie runs at 80% × 80% of the speed of Alice (0.80 × 0.80 = 0.64).

If Alice were to race against Charlie, then Charlie would be at 64m when Alice finished.

This means that Alice would beat Charlie by 36m.

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