Below, is one of the cleverest tests you will come across on the Internet. It has been around a bit, but maybe enough time has gone past that some of you have not seen this.
How many basketball passes does the team in white make?
This is NOT a trick question.
In the image above, which is the longer table?
Now measure them. Use a bit of paper ...
One of our favourites, below
We would often start programmes with executives, using this picture (amongst others).
A volunteer would read out what they saw, provided they thought there was nothing unusual. We would have this written on a flip chart.
We would invite someone who was sure there was nothing odd, to walk out and read each word touching it with their finger. The result was dramatic
If you can see nothing unusual about the image above, read it word by word, with your finger on each word in turn.
(Originally in Arthur Mee's Children's Encyclopaedia ... anyone remember that?
Find the hidden tiger.
We used to use the picture below with clients, to make the point that something that was right in front of them could be missed. The take away from an exercise like this was that the obvious is not always so obvious when you are expecting something different.
So in the picture below, find The Hidden Tiger. You will know - for sure - when you have found it. If in doubt ... you haven't.
Abdul Hadi Badi-al-Zamar, a Sufi, set off at dawn to climb a mountain. He left his trust steed, Aqil, tethered with food and water and set out as the sun peeped over the horizon.
He enjoyed the journey, following the single pilgrim path as it mounted past the Tomb of the Saint, and through the grove of beach trees, skirting the Lake of Tranquility, where he sat and ate his simple lunch, drinking from the lake's healing waters. He slept for a bit and then continued up, climbing the steps hewn into the rock-face, and stopping briefly to admire the view from the Great Cave with its wonderful frescoes of geometric designs. After reaching the top of the cliff he scrambled up the rock and stone strewn path till he reached the summit, exactly as the sun set.
He decided to spend the night on the mountain summit, meditating beneath the stars. This he did.
Abdul Hadi rose while it was stll dark, did his ablutions, and started his descent just as the sun peaked over the horizon. Again, during his descent, he stopped at various places, including the Buddhist Stupa, where he prayed briefly, the High Meadow, with its lovely mountain flowers, and once more, the Tomb of the Saint.
He reached the bottom of the mountain just at the moment the sun set.
The Sufi smiled to himself when greeted by one of his disciples. He explained that his journey up and his journey down the mountain had taken exactly the same time. The path was one, and he had never left it.
"Can you prove," he asked his disciple, "that there has to be one place, somewhere between the bottom and the top, where I was at exactly the same time of day, on the way up and the way down?"
His disciple thought for a moment, and then said, "No, it is not possible to prove that."
"Think again," said the Sufi, "it is certainly possible. It can be shown incontravertibly. What you or I cannot be sure of is where. But that it occurred there is no doubt."
The next day the disciple was very excited and said, "Yes. I can prove it."
And he could. Can you?
The proof offered by the disciple will be posted in about a week.
This problem was first posed by Arthur Koestler in his book, The Act of Creation.
For earlier problems posed by Sufi Abdul Hadi click on pictures below.
Abdul Hadi Badi-al-Zamar, the Sufi, arrived at the palace and was ushered in to see the princess.
"Come sit with me a while," she suggested, "and we will talk of the mysteries of life." They had known each other since she was a little girl, and Abdul Hadi admired her mind and delighted, to a degree that was proper, in her beauty. She displayed great promise as a mathematician.
"I have a problem for you," she said.
She clapped her hands together and her slave girl came in. "Bring the casket," she ordered, which the shapely young black woman did.
The princess sat up on her divan, opened the casket and poured its contents into a bowl, which pinged to the sound of falling pearls.
The slave girl, who must have known what was required, brought a pair of scales.
"The problem is this," she said to the old man, "one of these pearls is false. They all look identical, but one is fractionally lighter than the rest, and is not so valuable. Using just the scales and the pearls, what is the least number of weighings necessary to find the false pearl every time?
The Sufi rubbed his beard, and let the pearls trickle through his fingers, one by one, back into the bowl.
"With luck, one weighing would do it, but to be sure every time, then ..."
So, using just the scales and the pearls, no weights, how many times must the pearls be weighed to get the false pearl every time?
Abdul Hadi Badi-al-Zamar, a Sufi and mathematician, heard a ruckus ahead. Men were shouting at each other. “What ails thee?” he asked of one of the men, who was rending his clothing.
“Our father has just died,” said the man, “and left us with an insoluble problem.”
“What is the problem,” asked the Sufi, for he liked problems. They kept his mind nimble.
“Our father’s dying wish was as follows,” said the man, tears streaming down his face. “We were to divide our father’s horses as follows. I am the youngest, and I am to be given a ninth of the horses. My brother, Karim, is in the middle, and he is due one third of the horses. Our oldest brother, Malik is to receive one half.”
“How many horses do you have?" said the old Sufi, getting down of his own fiery steed.
Thirty-five,” said Nadir, the youngest of the brothers.
Malik, the oldest walked over and demanded, “Can you help us? If not, be on your way, and leave us to our misery, for we can see no solution, without butchering one or more of the beautiful stallions.”
“I think I can help you,” said the Sufi, “but first I must do something.”
He handed over the bridle of his horse to horse to Malik, who held it, frowning.
“Now let me see,” said the old man, while the three wives and numerous children gathered around. He picked up a stick and sketched some figures in the sand.
[If you wish to think about his solution, now is the time to do so … if not, then click on the link below to see Abdul Hadi Badi-al-Zamar’s elegant solution.]
Murray Morison is a novelist living in Crete
Posts can be reproduced in other blogs provided they are copied in full with a link back to this site.
When a teenage priestess, living 5,000 years ago in Ancient Egypt, connects with Rhory, an English schoolboy visiting the British Museum, she puts herself and him in grave danger.
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