Month: April 2026

Click on the link below to try the fun puzzle above – can you turn all the lights out for any size grid?

https://www.geogebra.org/m/xkcxt8bt

Square numbers

Triangular numbers

Square Triangular Numbers

1 appears on both lists so is a square triangular number.

0 could also be described as a square number (0x0) and is technically the first triangular number so 0 is also a square triangular number. 

Can you find any more square triangular numbers (numbers that appear on both lists)?

Solutions, notes and investigations are here.

Today we played a game where you have to take card and try and make 15 before your opponent. It relates to a game you have almost certainly played before. You could use playing cards to play and then discover the secret.

Here is a worksheet with all the rules and extensions to a hexagon puzzle, and the solutions to the hexagon are here.

We played a game posted on youtube by Mr Allen and extended it to different bases.

Set up

2-4 players. Using Ace -10 cards only.

Rules:

7 (or 6 if there are four of you) cards are placed face up for each player and two in the middle. The player who gets rid of their cards first wins.

You can put a card in the middle (on top of either pile) when one of your cards is an answer to an expression using the two cards in the middle. eg. if 6 and 2 are in the middle possible cards that can be played are: 8 (6+2) or 4 (6-2) or 3(6 2) or 2(6×2 – 12 is the answer but we use the last digit only).

Each player has to say the expression as they put the card down. eg 6 twos are 12 – placing the 2 or 6 minus 2 is 4. All players play on until no cards can be played. Then the dealer deals each player a card then put one on one of the two middle piles. Players then race to place cards until someone gets rid of all their cards!

Tasks

Play a few games of this and try some variations:

1. Instead of a race you could play in turn – competitively or collaboratively
2. Remove the 9s and 10s and play in mod 8
3. Also remove the 8s and play in mod 7

In the original game we used the last digit if the calculation was bigger than 10. This is equivalent to subtracting 10 until you have an answer that is the right size. This is called Mod 10. Mod 8 means that if you do e.g. 7 + 3 = 10 and get an answer that is too big you subtract 8 until it is the right size. 10 – 8 = 2.

More examples:  5 + 6 = 11 = 3

                             6 × 2 = 12 = 4

What is the best version (10,8 or 7) to play in terms of chances to play a card? You could use this worksheet to help you decide.