Creating a high number from this grid using minimal mathematical operations

Question

I'm creating a puzzle (pictured below). From this grid, how could I output a 10-digit number? The tiles cannot be moved or changed.

Instruction-wise, I would like to provide my players with some minimalist info about how to solve the puzzle, fitting onto a single Scrabble-size tile (see below). So far, the best I've come up with is having a double-sided Scrabble tile like this as a hint:

or

These give 63 x 11 = 693 and 28 x 28 = 784 (depending on whether you count the number of spots on tiles in all words placed in a particular direction - horizontal or vertical - or sum their tile values). Concatenating these together gives either 693784 or 784693.

This is a good start, but unfortunately these are only 6-digit numbers and I would like to get a 9- or 10-digit number (to mimic a phone number).

Any creative ideas for how I could achieve this, given the setup as in the main image above?

NOTE: I would prefer to use basic mathematical operations only (+, -, * and /) to make sure young teens can play the game.

Answer 1

Here's an approach that would use zero mathematical operations, bar basic addition...

It seems to me that the background to your photograph is just something that was lying around where you happened to assemble the tiles - but if the style of your puzzle allows it, the playing surface can be just as useful as the tiles themselves.

For example, you could construct a board that has particular regions indicated by coloured rectangles, with the expectation that the values of any tiles within those can be added up to form the digits for your phone number. For example, to make 555-1234567, and using a roughly rainbow-coloured ordering, you could design the game board to have something like this designed upon it:

Alternatively, you could use coloured markers around the edges to indicate that any values in similar-coloured rows or columns should be summed:

In fact, if using border markers you don't even need to use colours - you could use letters of the alphabet in order, or Greek alphabet characters even. Anything that might make a useful ordered key. This would also be a more friendly approach for players who may be colour-blind.

(Considering you are trying to provide players with minimal extraneous equipment, you could even just provide them with an accompanying 'key' image rather than a board itself. Or if using the second approach, you could give them two strips of paper, one for each axis, with the shapes/symbols on them; they would just need to align these strips with the grid.)

Don't forget that the playing tiles are not the only thing at your disposal here - the 'scenery' can be used!