Today’s puzzles start with a low-fi version of Countdown: you roll five dice and use basic arithmetic operations to get as close to a target number as possible.
Then the questions get a little trickier and a little more interesting.
1. Five pretty dice
A throw of five dice gives the numbers 1, 3, 4, 5 and 6.
I) Combining the numbers using +, -, x and ÷, which is closest to the goal of 55?
ii) What is the largest whole number you can reach?
iii) What is the largest whole number you can reach using only subtraction? (hint: this is a positive number.)
iv) What is the largest whole number you can reach using only division?
Clarification: By combining numbers, I mean creating an expression using addition, subtraction, multiplication, and division (and as many parentheses as you like.) For example, using the five numbers above, you can combine them like this: ((5×6) + 4) ÷ (3 – 1), which equals 17. You can use as many or as few plus, minus, time and division signs as you like . You must use all five numbers exactly once.
2. Five prettiest dice
You roll five standard dice.
I) What is the probability that the five numbers can be combined to reach 0?
ii) What is the probability that the maximum result is obtained simply by multiplying them all together?
iii) What is the probability that the maximum result is obtained just by multiplying them all together?
iv) What is the probability that the five random dice cannot be combined to reach any targets from 33 to 99?
Today’s issues are adapted from Math games with bad drawings, the new book from math communication superstar Ben Orlin. This is a beautifully produced compendium of math games that is destined to be a classic of popular math literature. Like his previous books, it has charming stick-figure sketches throughout.
The idea of the book is that mathematics can be fun – and social. Almost every game he writes about is for two or more players and should be enjoyed by anyone ages 10 and up.
For example, the game from which today’s puzzles are adapted is as follows. A player calls a number between 33 and 99. This is the target number. The player then rolls five dice. Now all players have two minutes to get as close to the target number as possible. Your score is your distance to the target and obviously lower scores are better.
I’ll be back at 5pm in the UK with the solutions. NO SPOILERS. Instead, please discuss your favorite math games.
UPDATE: You can now read the answers here.
Thanks to Ben Orlin. Math games with bad drawings is out now.
I install a puzzle here every two weeks on a Monday. I’m always on the lookout for great puzzles. If you want to suggest one, write to me.
I am the author of several puzzle books, the most recent the language lover’s puzzle book. I also give school lectures on math and puzzles (online and in person). If your school is interested, please contact us.
On Thursday, April 21, I will be giving a jigsaw workshop for the Guardian Masterclasses. You can register here.