My grandma has this game! I wanted to buy my own!
You turn them all over and put them into piles of 10. Separate the piles according to the amount of players.
Each player takes it in turns to flip over their top tile on the pile on the right hand side. The aim is to build up six piles from 1 to 20 in the middle.
If you turn over a tile and someone has a tile a number higher or lower (e.g. you flip over a 17 and someone else has a 16 or 18) you pass your tile over to put on their tile. The first player to get rid of all their tiles wins.
This is called Topps Tiles, great game and can’t find anything on the internet about it.
I have this game - the rules are as follows.
There are 120 tiles, 6 each numbered 1 to 20.
The aim of the game is to win by discarding all of your tiles first, either by placing them in the centre of the table on the "Centre stacks" or, better still, by placing them on your opponents "face up" stacks.
Share the 120 tiles face down between the players taking part - e.g. 40 tiles each for 3 players. Don't look at your tiles - keep them face down in front of you in one or two stacks.
Play consists, in the main, of forming 6 stacks of tiles in the centre of the table, each starting with 1, 2, 3 etc. and ending with 20. We shall call them "Centre Stacks".
(1) The youngest player takes the top tile of his stack and turns it over. If it is a 1, he places it in the centre of the table "face up" and takes his next tile. If this is a 2, he puts in on the 1 and carries on; or if it is another 1, he can start a new stack. The first tile that he cannot so place, he puts down, visible to all, as the starting tile of his "face up" stack. This ends his turn.
(2) Play continues but the game now includes each player's own "face up" stack and/or the "face up" stacks of his opponents. The next player continues as follows:
(a) First look whether you can place the top tile from your "face up" stack (if any) on one of your opponents. This can be done if it is the next highest or lowest number e.g. a 6 can be placed on a 5 or a 7.
(b) If (a) is not possible, look whether you can place the top tile from your "face up" stack (if any) on a "centre stack". This can be done if it is the next highest number e.g. a 4 can be placed on a 3. If you hold a 1, you may start a new stack.
(c) If (a) or (b) is not possible, turn over the top tile of your "face down" stack and try to act as in (a) and (b) above.
(d) If you are unsuccessful, place this tile on your "face up” stack.
(3) Whenever a player succeeds in placing a tile on an opponent’s "face up" stack or a "centre stack", he has another go. His turn ends when he has to place the tile on his own "face up" stack.
(4) PENALTY If a player does not observe rule 2 or makes a mistake, e.g. by placing an 8 on a 6, the other players shout "wrong" and each player hands him one of his tiles. They go on the wrong-doers "face up" stack.
(5) When a player has exhausted his "face down" stack, he turns over his "face up" stack and carries on.
(6) The player who first runs out of tiles is the winner.
The game you're searching is probably "Up and Down Donkey" (page 8 in the PDF)
It was used in math classes, and got sold commercially one time. Several rules existed to play with these tiles ;)