Here's how to solve the 'simple' high-school math problem stumping everyone on the internet

A question from a global math Olympiad for high-school children in Singapore is going viral after the question was leaked online.

The question seems simple — all you need to do is work out Cheryl's birthday, based on three statements and with just 10 possible dates to chose from — but the logic to solving it will really make your brain crinkle.

First, here's the question so you can have a go for yourself:

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Here's the question in plain text:

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates: May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, August 17.

Cheryl then tells Albert and Bernard separately the month and the day of her birthday, respectively.

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.

Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.

Albert: Then I also know when Cheryl’s birthday is.

So when is Cheryl’s birthday?

Think you know the answer? The question prompted so much confusion that the creators of the test posted an explanation on Facebook to clarify matters. 

The official solution is below. However, some commenters have found the logic even more confusing than the question itself, so we've broken it down even further below. 

Singapore and Asian School Math Olympiads/Facebook

If that solution confused you, we've broken it down piece by piece here:

• At the start, Albert and Bernard are each given one piece of information about Cheryl's birthday. Albert is given the month and Bernard is given the day. You have to assume that Cheryl was smart enough not give either of them a day or month that would enable them to work out the full date on their own.
• Now back to Bernard. Bernard knows the day (but not the month) the birthday falls on. We can rule out May 19 and June 18 straightaway because these days (18 and 19) occur only once in the list of dates. In contrast, 14, 15, 16, and 17 all appear twice. So, if Bernard was told either 18 or 19, he would be able to infer the month by knowing only the day. And that would be a different puzzle. So we can cross those two dates off the list.

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• But Albert knows that Bernard does not initially know the birthday. How? Well, Albert knows the month it falls in. Had Cheryl told Albert May or June (the only two months with unique number dates) then it's possible (but not guaranteed) that Bernard already knows the full date. But Albert knows that Bernard doesn't know the full date, which means Cheryl must have told Albert that the month is either July or August. So all other months get crossed off the list.

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• Bernard realises what the date is after Albert first says that he knowsthat Bernard doesn't know it. How does this work? Once Albert says that Bernard doesn't know, it shows to Bernard that it can't be in May or June. (After all, if it was, then Albert wouldn't know that Bernard doesn't know.) So this leaves July and August. Now, remember that Bernard knows the day (but not the month). Of the 5 options, 14 is the only one repeated twice. If it were July 14 or August 14 he still wouldn't know — but he does know, which means the day he was told must have been 15, 16, or 17, and we can cross another two possibilities out.

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• And then, after Bernard realises what the date is, Albert follows suit. This is because — as we've established — Albert knows only the month. With 3 options left, if Albert had been told it were in August, he still wouldn't know, because there are 2 August options left. But that's not the case — Albertdoes know with certainty what date it is. From this we can infer that it isJuly 16, as there's only one July option there.

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To recap, Albert was told that Cheryl's birthday was in July, while Bernard was told it landed on the 17. This limited knowledge allowed each to narrow down their options — and by making inferences from the other's ignorance, the two could continue to thin down the possible categories until there was only one option left.

By now, many people have chimed in to offer their own way of solving this math elimination problem and even an alternative answer of August 17 — to which the Singapore and Asian School Math Olympiads has also responded.

"If there are two possible answers, then this problem is ambiguous," the organisation said in a Facebook post.

Still, there are others who are willing to find the humour in all of this. One commenter writes: "I personally know Cheryl and her birthday is May 19."

7-S Framework McKinsey

Definition: 7-S Framework McKinsey

The McKinsey 7- S framework is a popular model used in organizations to analyse the environment to investigate if the company is achieving its intended objectives.

The name of the model can be explained by the fact that the model was developed by Tom Peters & Robert Waterman, consultants at the McKinsey & Company consulting firm.

The model proposes 7 interdependent factors – 3 hard ‘S’ i.e. strategy, structure, systems; and 4 soft ‘S’ i.e. shared values, skills, style and staff.

The hard ‘S’ are more tangible, easily to define and easy to influence than the soft ‘S’.

Strategy – It refers to the intended sequence of actions taken by a company to achieve its goals and objectives. It deals with resource allocation and includes competition, customers and the environment.
Structure – It refers to how the various business units are structured and how they communicate with each other. A company’s structure may be centralized or decentralized or may take many other forms depending on the company’s culture and values.

Systems – This includes a host of systems within an organization that define its processes and routines. It includes performance appraisal system, financial systems, IT systems etc.

Shared values – These are the core values of the company that connect all the other 6 factors. These are the fundamental ideas or guiding principles that lay the foundation of businesses.

Skills – These define the core competencies of the employees.

Style – This spans the core beliefs, norms and management style in the organization.

Staff – It refers to the number and type of employees in the organization. It is very important for an organization to manage its human capital to create competitive advantage.

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Definition: Brand Portfolio

The brand portfolio of a company is the complete range of all brands and brand lines it offers for sale in a particular category or market segment. A brand portfolio is said to be optimal when each brand in it has the ability to maximize equity in combination with all the other brands.

The basic principle of a brand portfolio is to maximize market coverage and to offer enough brands so that no potential customers feel left out, but at the same time to minimize overlap so that no two brands cannibalize each other. A good brand portfolio is marked by the clear differentiation of the component brands ad economy (Marketing and production costs are justified by the size of the end customer segment).

Brand portfolios must be continuously pruned, so as to identify weak brands, reenergize them or to kill off the unprofitable ones.

Within a portfolio, brands can play the following roles:

• Flankers (or fighters): Positioned with respect to the competitors’ brands so that the flagship or more important brands are protected. Care should be taken so as not to cannibalize the flagship brand.

• Cash cows: these may be showing falling sales but still command decent profits despite less marketing support.

• Low-end entry level: Relatively low-priced brands designed to attract the first-time consumer to the brand franchise. These customers can later be “traded up’ to higher-priced brands.

• High-end prestige: Higher-priced brands to add prestige and credibility to the entire portfolio