Can you solve it? Maths games with bad drawings

Today's puzzles begin with a low-fi version of Countdown, where you roll five dice and use basic operations to get as close to a target number as possible.

The questions get a bit more difficult.

1. There are five nice dice.

The numbers 1, 3, 4, 5 and 6 are produced by a roll of five dice.

What is the closest you can get to the target of 55?

What is the largest number you can reach?

What is the largest whole number you can reach with only one substitution?

What is the largest whole number you can reach using only division?

By combining the numbers, I mean creating an expression using addition, subtraction, multiplication and division. You could combine them in this way: ((5x6)+ 4), which is equal to 17. As you please, you can use as many, as few, plus, minus, times, and division signs as you please. You have to use all five numbers.

2. Five dice are nicer.

You roll dice.

Is there a chance the five numbers can reach 0?

Is the probability that the maximum result is obtained by combining them all together?

Is the probability that the maximum result is obtained uniquely by combining them all together?

The five random dice can't be combined to reach any of the targets.

Ben Orlin's new book, Math Games with Bad Drawings, is the basis for today's problems. A classic of popular mathematics literature is destined to be found in this compendium. His previous books have charming sketches of stick figures.

The idea of the book is that math can be fun and social. Most of the games he writes about are for two or more players, and are to be enjoyed by anyone over the age of 10.

The game from which today's puzzles are adapted is as follows. A player calls out a number. The target number is this. The player has five dice. The players have two minutes to get to the target number. Lower scores are better because they are closer to the target.

I will be back at 5pm UK with the solutions. There are noSPOILERS. Discuss your favourite games.

Thanks to Ben Orlin. There are math games with bad drawings.

On Mondays, I set a puzzle here. I always look for great puzzles. Email me if you would like to suggest one.

I'm the author of several books of puzzles, most recently the Language Lovers Puzzle Book. I give school talks about math and puzzles. Please contact your school if you are interested.

I will be giving a puzzles workshop on April 21. You can sign up here.