# Simple Math

Puzzles and brain teasers involving basic arithmetic and other simple math concepts – very little math knowledge required!

## Who Scored How Many Points

Lalo, Tyson, and Michael played a number of games of pick-up basketball. At the end, their combined points across all the games were:

• Lalo: 20
• Tyson: 10
• Michael: 9

They noticed that in every game, one of them scored x points, one of them scored y points, and one of them scored z points, where x > y > z and all three are distinct positive integers.

If Tyson got the highest score in the first game, who got the second highest score in the second game?

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## Double the Amount You Need to Do

At the beginning of January, you set a goal to work every day, to reach a total of 5000 minutes of work by the end of the month. But to give yourself a better shot of achieving this, you decide to front-load it—at the beginning of each day, you figure out how much you’d need to work on average on each remaining day to achieve your goal, and then you work double the amount you need to do. For example, if you had 50 minutes left and 5 days left, you would need to work 10 minutes/day, so you would choose to work 20 minutes on that 5th-to-last day.

If you chose to work this way, how long does it take you to complete your goal of 5000 minutes?

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## Five Points on a Line

There are five points on a line. You measure the distances between every pair of points and you find:

2, 4, 5, 7, 8, __, 13, 15, 17, 19

This list is ordered from shortest to longest. What is the missing distance?

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## Doubling Game

Three players gamble on a “doubling game.” In each round of the game, a single loser is determined, and this player has to double the money of the other two.

After three rounds of this game, each player has lost one round each, and each player now has \$24.

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## Giant Cat Army Riddle from TED-Ed

In Dan Finkel’s TED-Ed video, he shares this math puzzle, paraphrased as follows:

Dr. Schrödinger is creating an army of giant cats for villainous purposes. Your team of secret agents has located his lab, but needs to get through his unusual security system.

The system displays a single number, and has three buttons that control this number:

• Take the square root of the displayed number

Goal: make the numbers 2, 10, and 14 show on the display, in that order.

Rules:

• The display starts at 0.
• It’s fine if other numbers are displayed in between 2, 10, and 14, as long as they appear in that order.
• The system will malfunction if any number is displayed more than once.
• The system will malfunction if any number greater than 60 is displayed.
• The system will malfunction if any fraction/decimal is displayed.

How can you achieve this?

(Sorry, the giant cat army has nothing to do with the puzzle.)

Source: Dan Finkel and TED-Ed

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The “boy or girl paradox” is a well-known brain teaser by famous puzzle-maker Martin Gardner. It’s popularly considered a “paradox” because (1) it has a highly unintuitive solution, and (2) its ambiguous wording meant either of two solutions could be valid solutions.

This is a rewording of that brain teaser to eliminate some ambiguity from that original question:

Out of all families with exactly two children, we randomly pick one family that has at least one boy. What is the probability that both children in this family are boys?

Assume only for the purposes of this puzzle that a child can only be a boy or a girl, and that either possibility is equally likely.

The two envelopes paradox is a famous brain teaser of sorts, and not a true paradox. The problem is generally posed like this:

You are given a choice between two identical envelopes. One envelope contains some amount of money, and the other contains twice that amount of money. There is no way to distinguish between the two. However, when you choose one of the envelopes, before opening it, you are given the option of switching to the other envelope. Should you switch?

Why is this sometimes called a paradox? Well, if you choose to switch, you have a 50% chance of doubling your money, and a 50% chance of halving your money. If the amount of money in the envelope you initially chose is M, this reasoning suggests the expected amount in the other envelope is (2M + 0.5M) / 2 = 1.25M. This is more than M, so you should always switch.

But that would suggest once you’ve switched, you’re in the same position you were before you switched, so you should switch again. What is the problem with this reasoning?

## 7 Matchstick Equation Puzzles

In matchstick puzzles, you are presented with an incorrect equation made using matchsticks, and you must move 1 or more matchsticks to turn it into a valid equation.

You must use all of the matches, and you are not allowed to make an inequality symbol such as ≠, ≥, >, <, or ≤.

In each of these 7 fun matchstick equation puzzles, move exactly 1 match to fix the equation:

#### Click for Solution to 1 + 2 = 8

7 + 2 = 9

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