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Have you managed to find a solution? Do you consider yourself more intelligent than a 12-year-old?

Have you managed to find a solution? Do you consider yourself more intelligent than a 12-year-old?

Earlier today, I presented you with three puzzles designed for 12-year-olds. These puzzles were created by the charity Axiom Maths, which aims to support high-achieving children from low-income backgrounds in maintaining their academic success during their secondary school years.

1. Backwards multiplication

What is the four-digit number that becomes its own reverse when multiplied by 4? In other words, what are the values of a, b, c, and d such that abcd x 4 = dcba?

In this scenario, the variables a, b, c, and d represent distinct numerical values.

Solution 2178 x 4 = 8712

To complete STEP 1, the value of a must be either 1 or 2. This is due to the fact that multiplying a number greater than 3000 by four would result in a number with five digits, exceeding 12,000.

The solution must have an even value (as all numbers that are multiples of 4 are even) and therefore the value of a must be 2.

At STEP 3, we are aware that the product of 4 and d will result in a number ending in 2. By going through the four times table, we can determine that d is equal to either 3 or 8.

In order to satisfy the given condition, the value of d can only be 8 or 9. This is because when multiplied by 4, the result will be at least 8 thousand and something. Therefore, d must be 8. Additionally, in order for the product of 4 and b (potentially with a carry) to be less than 10, b can only be 1 or 2. Since b cannot be equal to a, it must be 1.

In the fifth step, the product of c multiplied by 4 and adding the carry of 3 results in a ones digit of 1. This means that the product of c and 4 must end in a units digit of 8. Therefore, c can only be either 2 or 7. Since c must be different from a, it must be 7.

2. Really secret Santa

Nine covert operatives, known as 001, 002, 003, 004, 005, 006, 007, 008, and 009, have arranged a Secret Santa gift exchange. The guidelines are encrypted to maintain the anonymity of the gift givers.

  • Agent 001 exchanges gifts with the agent who also gives a gift to Agent 002.

  • Agent 002 gives a present to the agent who gives a present to agent 003

  • Agent 003 is gifting the agent who gifts agent 004 with a present.

  • and so on, until

  • Agent 009 gifts Agent 001 in return for Agent 001’s gift.

From which agent will agent 007 receive her present?

Solution 002

One simple method for accomplishing this is to first draw a circle and then proceed to fill it in.

Bellos puzzle

Display the image in full-screen mode.

3. Trapezium, or trap-difficultum?

puzzleView image in fullscreen

Where should a vertical line be placed in a trapezium with two parallel horizontal sides to divide it into two equal areas?


Find the midpoint of each non-parallel edge. Find the midpoint of the line joining these two points. Put a vertical line through this point.

On both sides of the trapezium, the shaded and non-shaded triangles have the same area.View image in fullscreen

I trust that you have enjoyed these brainteasers. I will return in a fortnight.

To learn more about Axiom Maths, please refer to the original post or visit their website.

If you are a parent or school interested in participating in September 2024, please complete the Axiom Maths form provided.

This piece was updated on February 5, 2024. The correct response to the initial inquiry is 2178, not 2187 as stated in the previous version.

Since 2015, I have been posting a new puzzle every other Monday. I am constantly searching for interesting puzzles. If you have a suggestion, please email me.

Source: theguardian.com