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A swarm of dice bring nectar back to the hive from a domino garden. I just finished adding a new puzzle race game to Donimoes, my collection of domino puzzles and games, so I thought I would post a few bonus problems here. The game is Bee Donimoes, and the bees are dice flying back to the queen bee. Each die has to stay on the numbers that match it.

Equipment

  • a set of dominoes from double blank to double six
  • 4 six-sided dice

Object

Bring the nectar back to the hive in as few moves as possible. The biggest die is the queen bee and doesn't move, the others have to form a connected group around her.

Setup

Each problem has a diagram of the dominoes, so lay out the dominoes to match it. Look for the dominoes with a number at one end and a blank at the other. The number on each of those dominoes is the starting space for the die with the matching number. Take 3 dice, turn them so the numbers 1, 2, and 3 are on top, then place them on their starting spaces.

Here's an example setup with the dice added:

setup

Play

The die with the largest number is the queen bee, which never moves during the round. All the smaller bees have to bring their nectar back to her in one connected group. (Diagonal connections don't count.)

The dice can only land on their own numbers. They can move in two ways:

  1. In a straight line along a row or a column. They can pass over other numbers, squares with their own number, or other dice. This counts as one move.
  2. Changing direction over other dice. In the middle of a regular move, a die may make a 90° turn directly above another die. Later in the same move, it may make more turns directly above other dice. No matter how many turns it makes, this still counts as one move.

The blank on the other end of the queen bee's domino is wild. Any die can land there, if it's empty. A die may also leave the wild space on a later move.

Example Solution

Let's solve the set up above, where the 3 die is the queen bee. It seems best to start by moving the 2 where it can guide the 1 onto the wild spot:

Step 1

With the 2 in place, the 1 can get to its target.

Step 2

Finally, the 2 can complete the connected group with the help of the 1, in a nice leapfrog pattern.

Step 3

To describe each move, use the number of a die, a direction, and a distance, then add more directions and distances if the die turns corners. For example, 1R3 means move the 1 die to the right, 3 spaces. The solution above would be: 2D1, 1D3L3, 2L3U1.

Next Round

Put the dice back on their starting spaces. If there are any empty starting spaces, start the next round by adding the next bigger die on its starting space.

Today's Problem

Here's a problem to solve for today. Try to solve it in the fewest possible moves, and post your solution. The solution will include two rounds: three dice and four dice.

Monday problem

If you like this puzzle, watch for more challenging problems later in the week.

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  • $\begingroup$ We need to both place the dice in starting positions, and then move them around for minimum moves? $\endgroup$ – bobble Mar 22 at 14:53
  • $\begingroup$ That's correct, @bobble. The dice start in their starting positions, then move to form a connected group with the queen bee. The queen bee never moves. $\endgroup$ – Don Kirkby Mar 22 at 15:15
  • $\begingroup$ @bobble The starting spaces are explained in the Setup section (I missed it on my first read-through) $\endgroup$ – samm82 Mar 22 at 15:27
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Image Legend: White is a die location, Red is an unoccupied starting square, Blue is the wild space.

First round: (9 moves)

1 moves to activate 2: 1U3-R1D1-L3-U2-L1
Leapfrog: 2L2D4, 1D4R3, 2R3U2, 1U3
enter image description here

Second round: (9 moves)

3 gets in position to activate 1: 3L4-D1-R5
3 gets in position to activate 2: 1R2-U2L1, 3L5
Gathering: 1L4U2, 2L2D4, 1D3
enter image description here

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